London Mathematical Finance Group
London Mathematical Finance Group 

2015-16 London Mathematical Finance Seminar Series



The October-December 2015 programme is hosted by the Financial Mathematics and Risk and Stochastics groups at the London School of Economics and Political Science (LSE)

Date: Thursday 1 October 2015

Speaker #1: Markus Reiss, Humboldt University (!!! note the change of time and venue !!!)

Time: 16:00-17:00

Place: KCL - Strand Building, Room S0.13, Ground Floor

KCL Maps and Directions

Improved volatility estimation under one-sided errors with applications to limit order books

Abstract: For a semi-martingale X, which forms a stochastic boundary, a rate-optimal estimator for its quadratic variation <X,X> is constructed. The problem is embedded in a Poisson point process framework, which reveals an interesting connection to the theory of Brownian excursion areas. We derive n^{−1/3} as optimal convergence rate of integrated squared volatility estimation in a high-frequency framework with n observations (in mean). This considerably improves upon the classical n^{−1/4}-rate obtained for observations under centered noise. As an application estimating the integrated volatility of an efficient price process X from intra-day order book quotes is discussed.

Joint work with Markus Bibinger and Moritz Jirak

Speaker #2: Paolo Guasoni, Dublin City University (!!! note the change of time !!!)

Time: 17:30-18:30

Place: LSE - Thai Theatre, New Academic Building

LSE Maps and Directions

Who should sell stocks?

Abstract: Never selling stocks is optimal for investors with a long horizon and a realistic range of preference and market parameters, if relative risk

aversion, investment opportunities, proportional transaction costs, and dividend yields are constant. Such investors should buy stocks when their portfolio weight is too low, and otherwise hold them, letting dividends rebalance to cash over time rather than selling. With capital gain taxes, this policy outperforms both static buy-and-hold and dynamic rebalancing strategies that account for transaction costs. Selling stocks becomes optimal if either their target weight is low, or intermediate consumption is substantial.

(Joint work with Johannes Muhle-Karbe and Ren Liu)

Date: Thursday 15 October 2015

Speaker #1: Stéphane VilleneuveUniversity of Toulouse 1 Capitole

Time: 17:00-18:00

Place: LSE - Thai Theatre, New Academic Building

LSE Maps and Directions

Optimal exit under moral hazard

Abstract: We develop a model of optimal exit when a firm's asset owned by a risk-neutral principal is contracted out to a risk-neutral agent to manage. We characterize the optimal contract implementing effort at any time and prove that for a very profitable firm, it is optimal to let the agent shirk.

Keywords: Dynamic Principal-agent model, Optimal Stopping, Free boundary.

Speaker #2: Halil Mete Soner, ETH Zürich

Time: 18:15-19:15

Place: LSE - Thai Theatre, New Academic Building

LSE Maps and Directions

Stochastic target problems

Abstract: In a stochastic target problem, the controller tries to steer the state process into a prescribed target set with certainty. The state is assumed to follow stochastic dynamics while the target is deterministic and this miss-match renders the problem difficult. One exploits the degeneracies and/or the correlations of the noise process to determine the initial positions from which this goal is feasible. These problems appear naturally in several applications in quantitative finance providing robust hedging strategies. As a convenient solution technique, we use the geometric dynamic programming principle that we will describe in this talk. Then, this characterization of the reachability sets will be discussed in several examples.

Date: Thursday 29 October 2015

Speaker #1: Pierre Cardaliaguet, Université Paris-Dauphine

Time: 17:00-18:00

Place: LSE - Thai Theatre, New Academic Building

LSE Maps and Directions

Learning in mean-field games

Abstract: Mean field game systems describe equilibrium configurations in differential games with infinitely many infinitesimal interacting agents. The aim of this talk is to explain how such an equilibrium can appear: we introduce a learning procedure (similar to the fictitious play) and show its convergence when the mean field game is potential.

This is a joint work with S Hadikhanloo (Paris-Dauphine)

Speaker #2: Albina Danilova, LSE

Time: 18:15-19:15

Place: LSE - Thai Theatre, New Academic Building

LSE Maps and Directions

Markov bridges: SDE representation

Abstract: Please view the attachment here (PDF attachment).

Date: Thursday 12 November 2015

Speaker #1: Philipp Harms, ETH Zürich

Time: 17:00-18:00

Place: LSE - Thai Theatre, New Academic Building

LSE Maps and Directions

Affine representations of fractional processes with applications in mathematical finance

Abstract: Fractional processes have gained popularity in financial modelling due to the dependence structure of their increments and the roughness of their sample paths. The non-Markovianity of these processes gives, however, rise to conceptual and practical difficulties in computation and calibration. To address these issues, we show that a certain class of fractional processes can be represented as linear functionals of an infinite dimensional affine process. We demonstrate by means of several examples that the affine structure allows one to construct tractable financial models with fractional features.

Speaker #2: Marco Maggis, University of Milan

Time: 18:15-19:15

Place: LSE - Thai Theatre, New Academic Building

LSE Maps and Directions

Arbitrage theory without a reference probability: challenges of the model-free approach

Abstract: In a model independent discrete time financial market, we discuss the richness of the family of martingale measures in relation to different notions of Arbitrage, generated by a class S of significant sets. The choice of S reflects into the intrinsic properties of the class of polar sets of martingale measures. In particular: is S reduces to a singleton, absence of Model Independent Arbitrage is equivalent to the existence of a martingale measure; for S being the open sets, absence of Open Arbitrage is equivalent to the existence of full support martingale measures. These results are obtained by adopting a technical filtration enlargement and by constructing a Universal Aggregator of all arbitrage opportunities. Furthermore we prove the superhedging duality theorem, where trading is allowed with dynamic and semi-static strategies. We also show that the initial cost of the cheapest portfolio that dominates a contingent claim on every possible path might be strictly greater than the upper bound of the no-arbitrage prices. We therefore characterize the subset of trajectories on which this duality gap disappears and prove that it is an analytic set.

The talk will be based on two papers joint with M Burzoni and M Frittelli.

Date: Thursday 26 November 2015

Speaker #1: Denis Belomestny, Duisburg Essen University

Time: 17:00-18:00

Place: LSE - Thai Theatre, New Academic Building

LSE Maps and Directions

Higher order variance reduction for discretised diffusions via regression

Abstract: In this talk we present a novel approach towards variance reduction for discretised diffusion processes. The proposed approach involves specially constructed control variates and allows one to reduce the variance up to a certain power of discretisation error. In this way the complexity order of the plain MC algorithm can be reduced down to epsilon^{-2+delta} for any delta in [0,0.5) with epsilon being the precision to be achieved. These theoretical results are illustrated by several numerical examples.

Speaker #2: Ulrich Horst, Humboldt University

Time: 18:15-19:15

Place: LSE - Thai Theatre, New Academic Building

LSE Maps and Directions

Conditional analysis and a principal agent problem

Abstract: We analyse conditional optimization problems arising in discrete-time dynamic Principal-Agent models of delegated portfolio management. In these models, an investor (the Principal) outsources her portfolio selection to a manager (the Agent) whose investment decisions the investor cannot or does not want to monitor. We prove that if both parties' preferences are time-consistent and translation invariant and under suitable assumptions on the class of admissible contracts the problem of dynamic contract design can be reduced to a series of one-period conditional optimization problems of risk-sharing type under constraints, that the first-best solution is implementable if it exists and that optimal contracts must generally make use of derivatives. We fully solve the dynamic contracting problem for a class of optimized certainty equivalent (OCE) utilities including expected exponential utilities and Average Value at Risk. If information is generated by finitely many random walks, then our conditional optimization problems reduce to standard optimization problems in Euclidean spaces. In this case derivatives are not part of optimal compensation schemes and the contracting problem can be solved for all OCE utilities.

The talk is based on joint work with Julio Backhoff.

Date: Thursday 10 December 2015

Speaker #1: Peter Bank, TU Berlin

Time: 17:00-18:00

Place: LSE - Thai Theatre, New Academic Building

LSE Maps and Direction

Optimal investment with price impact

Abstract: We consider a financial model with price impact where a large investor’s orders affect bid and ask prices. In a Brownian setting with exponential utility, this model allows for an explicit description of optimal investment strategies. In order to learn about indifference pricing and hedging of financial derivatives in such a frictional model, we consider a quadratic benchmark problem which emerges heuristically as the high-resilience limit of the original model. The benchmark problem also allows for a closed-form solution for very completely general options. It turns out that, rather than trading towards the currently optimal position from a frictionless reference model, it is optimal to trade towards a properly weighted average of this positions future expected values. This is joint work in progress with Mete Soner and Moritz Voss.

Speaker #2: Peter Tankov, Université Paris-Diderot (Paris 7)

Time: 18:15-19:15

Place: LSE - Thai Theatre, New Academic Building

LSE Maps and Directions

Asymptotic lower bounds for optimal trading

Abstract: We consider the problem of tracking a target whose dynamics is modelled by a continuous Itô semi-martingale. The aim is to minimize both deviation from the target and tracking efforts. We establish the existence of asymptotic lower bounds for this problem, depending on the cost structure. These lower bounds can be related to the time-average control of Brownian motion, which is characterized as a deterministic linear programming problem. We provide a comprehensive list of examples with explicit expressions for the lower bounds and discuss the application of our results to the problem of optimal trading in the presence of transaction costs.

The January-March 2016 programme is hosted by the King's College London.

The seminar is partially supported by INTECH

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Date: Thursday 21 January 2016

Speaker #1: Luciano Campi, LSE

Time: 16:15-17:00

Place: King's College London- Nash Lecture Theatre K2.31

Find out more information of Luciano Campi here

On the support of extremal martingale measures with given marginals

After discussing some characterisations of extremal measures with given marginals available in the literature, going from functional analysis to combinatorics, we will turn to their martingale counter-parts whose study is related to robust pricing and hedging. In particular, we will give some sufficient and necessary conditions with a geometric and combinatorial flavour for a given set to be the support of an extremal martingale measure with pre-specified discrete marginals. Some open problems will be discussed as well. This is based on joint work with Claude Martini.

Speaker #2: Ying Hu Université de Rennes 1

Time: 17:15-18:00

Place: King's College London- Nash Lecture Theatre K2.31

Find out more information of Ying Hu here

An ergodic BSDE approach to large time behaviour of solution of semilinear parabolic partial differential equation

This talk is devoted to the study of the large time behaviour of solution of some semilinear parabolic partial differential equation (with Dirichlet or Neumann boundary condition). A probabilistic method (more precisely, an approach via an ergodic backward stochastic equation) is developped to show that the solution of a parabolic semilinear PDE at large time $T$ behaves like a linear term $\lambda T$ shifted with a function $v$, where $(v,\lambda)$ is the solution of the ergodic PDE associated to the parabolic PDE. The advantage of our method is that it gives an explicit rate of convergence. The result gives a perspective to give a precise estimate on the long run asymptotics for utility maximisation.

Date: Thursday 4 February 2016

Speaker #1: Jakša Cvitanić, Caltech

Time: 16:15-17:00

Place: King's College London- Nash Lecture Theatre K2.31

Find out more information about Jakša Cvitanić here

Dynamic Programming Approach to Principal-Agent Problems and Applications in Portfolio Management

We develop a new approach to solving a general finite horizon Principal-Agent problem from Contract Theory. We identify a family of admissible contracts for which the optimal agent's action is explicitly characterized; then, we show that we do not lose on generality when finding the optimal contract inside this family. Our argument relies on the Backward Stochastic Differential Equations approach to non-Markovian stochastic control, and more specifically, on the most recent extensions to the second order case. As a special case example, we apply the method to the problem of optimal compensation of a portfolio manager.

Joint with N. Touzi and D. Possamai

Speaker #2: Miklós Rásonyi, MTA Alfréd Rényi Institute of Mathematics

Time: 17:15-18:00

Place: King's College London- Nash Lecture Theatre K2.31

Find out more information about Miklós Rásonyi here

Sticky processes with jumps

We prove that sticky processes can be approximated arbitrarily well in L_p norm by processes that are martingales under an equivalent change of measure. The precise formulation of this result raises several issues which we will discuss. We also present some applications to the theory of illiquid markets.

Date: Thursday 18 February 2016

Speaker #1: Fabio Bellini, Università degli Studi di Milano-Bicocca

Time: 16:15-17:00

Place: King's College London- Nash Lecture Theatre K2.31

Find out more about Fabio Bellini here

Elicitability, expectiles and backtesting with loss functions

We review the notion of elicitable statistical functional and discuss the characterisation of expectiles as the only elicitable coherent risk measures. We investigate the financial interpretation of expectiles and their possible use as risk measures for capital requirements, in comparison with the more established Value at Risk and Expected Shortfall. Finally, we discuss how consistent loss functions, whose existence is guaranteed by the elicitability property, may be used for testing and assessing the accuracy of a risk forecasting model.

Speaker #2: Jan Obloj, University of Oxford

Time: 17:15-18:00

Place: King's College London- Nash Lecture Theatre K2.31

Find out more about Jan Obloj here

Robust pricing-hedging duality with path constraints and applications to information quantification

We consider robust (pathwise) approach to pricing and hedging. Motivated by the notion of prediction set in Mykland (2003), we include in our setup modelling beliefs by allowing to specify a set of paths to be considered, e.g. super-replication of a contingent claim is required only for paths falling in the given set. The framework interpolates between model--independent and model--specific settings. We establish a general pricing--hedging duality. The setup is parsimonious and includes the case of no traded options as well as the so-called martingale optimal transport duality of Dolinsky and Soner (2013) which we extend to multiple dimensions and multiple maturities. In presence of non-trivial beliefs, the equality is obtained between limiting values of perturbed problems indicating that the duality holds only if the market is stable under small perturbations of the inputs. Our framework allows to quantify the impact of making assumptions or gaining information. We focus in particular on the latter and study if the pricing-hedging duality is preserved under additional information.

Joint work with Zhaoxu Hou and Anna Aksamit.

Date: Thursday 3 March 2016

Speaker #1: Marco Fritelli, Università degli Studi di Milano

Time: 16:15-17:00

Place: King's College London- Nash Lecture Theatre K2.31

Find out more about Marco Fritelli here

A Unified Approach to Systemic Risk Measures via Acceptance Sets

The purpose of this paper is to specify a general methodological framework that is flexible enough to cover a wide range of possibilities to design systemic risk measures via multi-dimensional acceptance sets and aggregation functions, and to study corresponding examples. Existing systemic risk measures can usually be interpreted as the minimal amount of cash needed to secure the system after aggregating individual risks. In contrast, our approach also includes systemic risk measures that can be interpreted as the minimal amount of cash that secures the aggregated system by allocating capital to the single institutions before aggregating the individual risks. An important feature of our approach is the possibility of allocating cash according to the future state of the system (scenario-dependent allocation). We illustrate with several examples the advantages of this feature. We also provide conditions which ensure monotonicity, convexity, or quasi-convexity of our systemic risk measures.

Speaker #2: Matthias Scherer, Technische Universität München (TUM)

Time: 17:15-18:00

Place: King's College London- Nash Lecture Theatre K2.31

Find out more about Matthias Scherer here

Exogenous shock models in high dimensions and a primer on model robustness

We review recent results on exogenous shock models and show how interesting subfamilies can be constructed in high dimensions. This is needed for applications in portfolio-credit risk and insurance. From a mathematical perspective, it bridges concepts from stochastic processes, self-similar distributions, and multivariate probability laws. Another-less obvious- application of the theory is the problem of model robustness in market risk management, for which we propose a new philosophy based on a distortion of the stochastic root of a risk model. The talk is based on joint work with Jan-Frederik Mai and Steffen Schenk.

Date: Thursday 17 March 2016

Speaker #1: Josef Teichmann, ETH Zürich

Time: 16:15-17:00

Place: King's College London- Nash Lecture Theatre K2.31

Find out more about Josef Teichmann here

Rough Term structures

In the realm of Martin Hairer's regularity structures we introduce a Sobolev type norm on spaces of modelled distributions to enable the proper use of methods from stochastic analysis. We show several examples from term structure theory where regularity structures might be of importance in mathematical Finance.
(joint work with David Proemel, ETH)

Speaker #2: Philipp Keller, Deloitte

Time: 17:15-18:00

Place: King's College London- Nash Lecture Theatre K2.31

Find out more about Philipp Keller here

The foundations of the valuation of insurance liabilities

Valuation of liabilities is at the core of insurers’ risk management and determines the type of products that are being sold by insurers and their investment strategies. Accounting and regulatory valuation frameworks impact the entire financial market and society. Often insurers cover policyholders from a wide variety of risks over many decades, which makes the valuation of these covers highly complex and challenging.

We discuss the purposes of different valuation frameworks that are being used by insurance companies and put the different types of valuation standards into the context of replication with financial instruments to show their differences and commonalities. We focus on economic, market consistent valuation which is based on the cost of producing insurance liabilities with traded financial instruments and on consistency requirements between best estimates, the cost of capital and discount rates.

Finally, we give an overview over the connection between valuation, systemic risk and macroprudential policies and regulations of central banks.

Date: Thursday 31 March 2016

Speaker #1: Aleksandar Mijatovic, King's College London

Time: 16:15-17:00

Place: King's College London- Nash Lecture Theatre K2.31

Find out more about the speaker here

A weak multilevel Monte Carlo scheme for multidimensional L\'evy-type processes

Abstract: In this talk we describe a novel weak multilevel approximation scheme for time-changed L\'evy processes and L\'evy driven SDEs. The scheme is based on the state space discretisation of the driving L\'evy process and is particularly well suited if the multidimensional driver is given by a L\'evy copula.The multilevel version of the scheme is genuinely weak as it does not require strong convergence to control the level variances. The analysis of the level variances rests upon a new coupling between the approximating Markov chains of the consecutive levels, which is defined via a coupling of the corresponding Poisson Point Processes and is easy to simulate.

This is joint work with D. Belomestny.

Speaker #2: Martino Grasselli, Finance Lab at the Pôle Universitaire Léonard de Vinci / Università Degli Studi di Padova

Time: 17:15-18:00

Place: King's College London- Nash Lecture Theatre K2.31

Find out more about Martino Grasselli here

Lie Symmetry Methods for Local Volatility Models

We investigate PDEs which are associated with the calculation of expectations for a large class of Local Volatility Models. We find nontrivial symmetry groups that can be used to obtain standard integral transforms of fundamental solutions of the PDE. We detail explicit computations in the separable volatility case when σ(t, x) = h(t)(α + βx + γx2), corresponding to the so called Quadratic Normal Volatility Model. We also consider choices for which exact fundamental solutions can be obtained.

Date: Thursday 23 June 2016

Speaker #1: Lan WU, Peking University 

Time: 16:00-17:00

Place: King's College London- Strand Building, S4.23

Find out more about the speaker here

Occupation Times of General Lévy Processes

Abstract: For a general Lévy process X which is not a compound Poisson process, we are interested in its occupation times. We use a quite novel and useful approach to derive formulas for the Laplace transform of the joint distribution of X and its occupation times. Our formulas are compact, and more importantly, the forms of the formulas clearly demonstrate the essential quantities for the calculation of occupation times of X. It is believed that our results would play an important role in financial applications.

The January-March 2015 programme is hosted by University College London (UCL). 

The seminar is partially supported by INTECH.

Date: 15 January 2015

Speaker: Andrew Papanicolaou, University of Sydney

Time: 16:30-17:30


Title: Perturbation Analysis for Investment Portfolios Under Partial Information with Expert Opinions

Abstract: We analyze the Merton portfolio optimization problem when the growth rate is an unobserved Gaussian process whose level is estimated by filtering from observations of the stock price. We use the Kalman filter to track the hidden state(s) of expected returns given the history of asset prices, and then use this filter as input to a portfolio problem with an objective to maximize expected terminal utility. Our results apply for general concave utility functions. We incorporate time-scale separation in the fluctuations of the returns process, and utilize singular and regular perturbation analysis on the associated partial information HJB equation, which leads to an intuitive interpretation of the additional risk caused by uncertainty in expected returns.The results are an extension of the partially-informed investment strategies obtained by the Black-Litterman model, wherein investors' views on upcoming performance are incorporated into the optimization along with any degree of uncertainty that the investor may have in these views.

Speaker: Christoph Kuehn, J.W. Goethe-Universität, Frankfurt

Time: 17:45-18:45


Title: Modeling capital gains taxes in continuous time

Abstract: In most countries, trading gains have to be taxed. The modeling is complicated by the rule that gains on assets are taxed when assets are sold and not when gains actually occur. This means that an investor can influence the timing of her tax payments, i.e., she holds a timing option. In this talk, it is shown how the tax payment stream can be constructed beyond trading strategies of finite variation. We give an example for tax-efficient strategies for which the tax payment stream can be computed explicitly and show for which trading strategies the tax payment process is of (in)finite variation. Finally, we solve an optimal stopping problem that illustrates the basic effect of taxes on optimal investment decisions. This confirms the conjecture that the value of the tax-timing option is increasing in the volatility of the asset the investor holds. (The talk is based on joint work with Björn Ulbricht and partly with Budhi Arta Surya)

Date: 29 January 2015

Speaker: Damiano Brigo, Imperial College London

Time: 16:30-17:20


Title: Nonlinear valuation under credit gap risk, collateral margins, funding costs and multiple curves

Abstract: Following a quick introduction to derivatives markets and the classic theory of valuation, we describe the changes triggered by post 2007 events. We re-discuss the valuation theory assumptions and introduce valuation under counterparty credit risk, collateral posting, initial and variation margins, and funding costs. A number of these aspects had been investigated well before 2007. We explain model dependence induced by credit effects, hybrid features, contagion, payout uncertainty, and nonlinear effects due to replacement closeout at default and possibly asymmetric borrowing and lending rates in the margin interest and in the funding strategy for the hedge of the relevant portfolio. Nonlinearity manifests itself in the valuation equations taking the form of semi-linear PDEs or Backward SDEs. We discuss existence and uniqueness of solutions for these equations. We present an invariance theorem showing that the final valuation equations do not depend on unobservable risk free rates, that become purely instrumental variables. Valuation is thus based only on real market rates and processes. We also present a high level analysis of the consequences of nonlinearities, both from the point of view of methodology and from an operational angle, including deal/entity/aggregation dependent valuation probability measures and the role of banks treasuries. Finally, we hint at how one may connect these developments to interest rate theory under multiple discount curves, thus building a consistent valuation framework encompassing most post-2007 effects.

Speaker: Claude Martini, Zeliade Systems

Time: 17:45-18:35


Title: Investigating the extremal martingale measures with pre-specified marginals

Abstract: The extremal points in the set of all measures with pre-specified marginals, without the martingale constraint, have been extensively studied by many authors in the past (e.g. Denny, Douglas, Letac, Klopotowski to cite only a few). In this talk, we will focus on the characterization provided by Denny in the countable case: a key property is that the support of the probability Q has no “cycle”, otherwise a perturbation of Q can be constructed so that Q can not be extremal. In the context of the 2 marginals martingale problem studied by Beiglböck-Juillet, with special cases provided by Henry-Labordère and Touzi, Hobson and Klimmeck, Hobson and Neuberger, and Laachir, we give examples of extremal and non-extremal points, and give partial results towards a characterization theorem. (Joint work with L. Campi, LSE)

Date: 12 February 2015

Speaker: Julien Hugonnier, EPFL

Time: 16:30-17:20


Title: Heterogeneity in Decentralized Asset Markets

Abstract: We study a search and bargaining model of an asset market, where investors’ heterogeneous valuations for the asset are drawn from an arbitrary distribution. Our solution technique renders the analysis fully tractable and allows us to provide a full characterization of the equilibrium, in closed form, both in and out of steady state. We use this characterization for two purposes. First, we establish that the model can naturally account for a number of stylized facts that have been documented in empirical studies of over-the-counter asset markets. In particular, we show that heterogeneity among market participants implies that assets are reallocated through “intermediation chains,” ultimately producing a core-periphery trading network and non-trivial distributions of prices and trading times. Second, we show that the model generates a number of novel results that underscore the importance of heterogeneity in decentralized markets. We highlight two: first, heterogeneity magnifies the price impact of search frictions; and second, search frictions have larger effects on price levels than on price dispersion. Hence, quantifying the price discount or premium created by search frictions based on observed price dispersion can be misleading.

Speaker: Matthieu Rosenbaum, Université Pierre et Marie Curie

Time: 17:45-18:35


Title: Volatility is rough

Abstract: Estimating volatility from recent high frequency data, we revisit the question of the smoothness of the volatility process. Our main result is that log-volatility behaves essentially as a fractional Brownian motion with Hurst exponent H of order 0.1, at any reasonable time scale. This leads us to adopt the fractional stochastic volatility (FSV) model of Comte and Renault. We call our model Rough FSV (RFSV) to underline that, in contrast to FSV, H<1/2. We demonstrate that our RFSV model is remarkably consistent with financial time series data; one application is that it enables us to obtain improved forecasts of realized volatility. Furthermore, we find that although volatility is not long memory in the RFSV model, classical statistical procedures aiming at detecting volatility persistence tend to conclude the presence of long memory in data generated from it. This sheds light on why long memory of volatility has been widely accepted as a stylized fact. Finally, we provide a quantitative market microstructure-based foundation for our findings, relating the roughness of volatility to high frequency trading and order splitting. This is joint work with Jim Gatheral and Thibault Jaisson.

Date: 26 February 2015

Speaker: Stefan Ankirchner, Universität Jena

Time: 16:30-17:20


Title: A generalized Donsker theorem and approximating SDEs with irregular coefficients

Abstract: We provide a new method for approximating the law of a diffusion M solving a stochastic differential equation with coefficients satisfying the Engelbert-Schmidt conditions. To this end we construct Markov chains whose law can be embedded into the diffusion M with a sequence of stopping times that have expectation 1/N, where N is a discretization parameter.
The transition probabilities of the Markov chains are determined by a reference probability measure, scaled with a factor depending on N and the state. We show that the Markov chains converge in distribution to the diffusion M, thus refining the Donsker-Prokhorov invariance principle. For some cases we provide a convergence rate. Finally, we illustrate our results with several examples. The talk is based on joint work with Thomas Kruse and Mikhail Uruso

Speaker: Bruno Bouchard, Université Paris-Dauphine

Time: 17:45-18:35


Title: Almost-sure hedging with permanent price impact


We consider a financial model with permanent price impact. Continuous time trading dynamics are derived as the limit of discrete rebalancing policies. We then study the problem of super-hedging a European option. Our main result is the derivation of a quasi-linear pricing equation. It holds in the sense of viscosity solutions. When it admits a smooth solution, it provides a perfect hedging strategy.

Date: 12 March 2015

Speaker: Ulrich Horst, Humboldt-Universität, Berlin

Time: This talk has been cancelled.

Title: Weak law of large numbers for a limit order book model with fully state dependet order dynamics

Abstract: We study a one-sided limit order book (LOB) model, in which the order dynamics depend on both, the current best bid price and the current volume density function. For the joint dynamics of the best bid price and the standing buy volume density we derive a weak law of large numbers, which states that the LOB model converges to a continuous-time limit when the size of an individual order as well as the tick size tend to zero and the order arrival rate tends to infinity. In the scaling limit the standing buy volume density follows a non-linear PDE coupled with a non-linear ODE that describes the best bid price. The talk is based on joint work with Doerte Kreher.

Speaker: Huyên Pham, Université Paris-Diderot

Time: 17:45-18:35


Title: An optimal trading problem in intraday electricity markets


We consider the problem of optimal trading for a power producer in the context of intraday electricity markets. The aim is to minimize the imbalance cost induced by the random residual demand in electricity, i.e. the consumption from the clients minus the production from renewable energy. For a simple linear price impact model and a quadratic criterion, we explicitly obtain approximate optimal strategies in the intraday market and thermal power generation, and exhibit some remarkable properties of the trading rate. Furthermore, we study the case when there are jumps on the demand forecast and on the intraday price, typically due to error in the prediction of wind power generation. Finally, we solve the problem when taking into account delay constraints in thermal power production. Based on joint work with René Aid (EDF) and Pierre Gruet (Paris Diderot).

Date: 19 March 2015

Speaker: Thaleia Zariphopoulou, University of Texas at Austin

Time: 16:30-17:20


Title: Forward investment performance processes: review and open problems

Abstract:In this talk, I will discuss the concept of forward investment performance process and will present results on discrete and continuous time. The latter are related to a fully-non linear SPDE, and to ergodic and infinite horizon BSDE. I will also state some open problems in asset allocation under these alternative criteria.

Date: 26 March 2015

Speaker: Tomasz BieleckiIllinois Institute of Technology

Time: This talk has been cancelled.


Title: Market making via sub-scale invariant Dynamic Acceptability Indices

Abstract: The main goal of this study is to develop a general theoretical pricing framework that will capture some practically relevant properties, such as: the prices are not homogeneous in number of shares traded; the underlying securities bear transaction costs; the securities pay dividends; the dividends may be different for a long or short position. To achieve this goal, we use sub-scale invariant Dynamic Acceptability Indices (DAIs) as the main tool in developing thepricing methodology, and consequently, we present a representation of proposed prices in terms of a class of Backward Stochastic Difference Equations and g-Expectations. Besides the above mentioned properties, we also prove that: considered market models do not admit arbitrage; bid and ask prices do shrink the super hedging pricing interval; the prices are time consistent in some appropriate sense; if the drivers are linear we recover the classical martingale pricing theory. Finally, we provide some practical examples.

Speaker: Ernst Eberlein, University of Freiburg

Time: 17:45-18:35


Title: Lévy driven two price valuation with applications to long-dated contracts


In the classical valuation theory the law of one price prevails and market participants trade freely in both directions at the same price. This approach is appropriate for highly liquid markets. In the absence of perfect liquidity the law of one price should be replaced by a two price valuation theory where market participants continue to trade freely with the market but the terms of trade now depend on the direction of the trade. We develop here a static as well as a continuous time theory for two price economies. The two prices are termed bid and ask or lower and upper price but they should not be confused with the literature relating bid-ask spreads to transaction costs or other frictions involved in modeling financial markets. The bid price arises as the infimum of test valuations whereas the ask price is the supremum of such valuations. The two prices are related to nonlinear expectations. Probability as well as measure distortions are used to make this approach operational. We consider specific models where the uncertainty is given by purely discontinuous Lévy processes. The approach is illustrated to price stochastic perpetuities, i.e. contracts with no apparent maturity, and to value compound Poisson processes of insurance loss liabilities. This is joint work with Dilip Madan, Martijn Pistorius, Wim Schoutens and Marc Yor.


The May-June 2015 programme is hosted by the Finance Faculty at Cass Business School, City University London

Date: 21 May 2015

Speaker: Giovanni PuccettiUniversity of Milan

Time: 18:10 - 19:00


Title: Reducing model risk via additional (in)dependence assumptions

Abstract: We derive lower and upper bounds for the Value-at-Risk of a portfolio of losses when the marginal distributions are known and an additional (in)dependence structure is assumed. We provide several actuarial examples showing that the newly proposed bounds strongly improve those available in the literature that are based on the sole knowledge of the marginal distributions. This talk is based on joint works with Valeria Bignozzi, Daniel Small, Ludger Rüschendorf and Steven Vanduffel.

Date: 18 June 2015

Speaker: Steven Kou, National University of Singapore

Time: 17:00 - 17:50


Title: Separating Skilled and Unskilled Fund Managers by Contract Design

Abstract: Foster and Young (2010, Quarterly Journal of Economics) shows that it is very difficult to design performance fee contracts rewarding skilled fund managers while screening out unskilled fund managers. In particular, none of the standard practices, such as postponing bonuses and claw-back provisions, can separate skilled and unskilled managers. We show that if (1) there is a liquidation boundary, meaning that the fund investors will close the fund immediately if the fund return is bad enough to hit the boundary, and (2) the fund manager has to use his/her own money to set up a deposit to offset the potential losses from the fund investors, then the skilled and unskilled fund managers can be separated. The deposit can be a combination of cash or an equity stake in the fund. A particular version of this type of contracts, called the first-loss scheme, is quite popular in China, and is emerging in U.S. This is joint work with Xuedong He and Sang Hu.

Speaker: David P. Newton, Nottingham University Business School

Time: 18:10 - 19:00


Title: Advancing the universality of numerical integration methods to any underlying process for option pricing

Exceptional accuracy and speed for option pricing are available via quadrature (Andricopoulos et al., JFE, 2003), extending into multiple dimensions with complex path-dependency and early exercise (Andricopoulos et al., JFE, 2007). However, the technique was incomplete, leaving many modelling processes outside the Black-Scholes-Merton framework unattainable. In this seminar paper (following Chen, Harkonen and Newton, JFE, 2014), I discuss how to remove the remaining major block to universal application. Although this had appeared highly problematic, the solution turns out to be conceptually simple and implementation is straightforward. Crucially, the method retains its speed and flexibility across complex combinations of option features but is now applicable across other underlying processes.

2014-15 seminar series


The October-December 2014 programme is hosted by King's College London

Date: 9 October 2014

Speaker: Sam Cohen, University of Oxford

Time: 16:30-17:30

Place: Strand Campus, S-1.27 (1st basement, Strand Building)

Title: Ergodic BSDEs with Lévy noise and time dependence

Abstract: In many control situations, particularly over the very long term, it is sensible to consider the ergodic value of some payoff. In this talk, we shall see how this can be studied in a weak formulation, using the theory of ergodic BSDEs. In particular, we shall consider the case where the underlying stochastic system is infinite dimensional, has Lévy-type jumps, and is not autonomous. We shall also see how this type of equation naturally arises in the valuation of a power plant.

Speaker: Sergei Levendorskiy, University of Leicester

Time: 17:45-18:45

Place: Strand Campus, S-1.27 (1st basement, Strand Building)

Title: Efficient Laplace and Fourier inversions and Wiener-Hopf factorization in financial applications

Abstract: A family of (quasi-) parabolic contour deformations increases the speed and accuracy of calculation of fairly complicated oscillatory integrals in option pricing formulas in many cases when standard approaches are either too slow or inaccurate or both. Variations: quasi-asymptotic formulas that are simple and much faster than general formulas, and which, for typical parameter values, are fairly accurate starting from relatively small distances from the barrier and maturities more than a year. When several Laplace and Fourier inversions are needed, it is necessary to use a family of contour transformations more flexible than Talbot's deformation of the contour in the Bromwich integral. Further step in a general program of study of the efficiency of combinations of one-dimensional inverse transforms for high-dimensional inversions [Abate-Whitt, Abate-Valko and others].

Calculations of Greeks and pdf can be made much more accurate; the latter can be used for fast Monte-Carlo simulations (faster than Madan-Yor method). Examples when insufficiently accurate pricing procedures may prevent one to see a good model (“sundial calibration”) or to see a local minimum of the calibration error when there is none, and the model may be unsuitable (“ghost calibration”) will be presented.

Date: 23 October 2014

Speaker: Jan Kallsen, University of Kiel

Time: 16:30-17:30

Place: Strand Campus, S-1.27 (1st basement, Strand Building)

Title: On portfolio optimization and indifference pricing with small transaction costs 

Abstract: Portfolio Optimization problems with frictions as e.g. transaction costs are hard to solve explicitly. In the limit of small friction, solutions are often of much simpler structure. In the last twenty years, considerable progress has been made both in order to derive formal asymptotics as well as rigorous proofs. However, the latter usually rely on rather strong regularity conditions, which are hard to verify in concrete models. Some effort is still needed to make the results really applicable in practice. This talk is about a step in this direction. More specifically, we discuss portfolio optimization for exponential utility under small proportional transaction costs. As an example, we reconsider the Whalley-Willmott results of utility-based pricing and hedging in the Black-Scholes model. We relax the conditions required by Bichuch who gave a rigorous proof for smooth payoffs under sufficiently small risk aversion.

Speaker: Martijn Pistorius, Imperial College London

Time: 17:45-18:45

Place: Strand Campus, S-1.27 (1st basement, Strand Building)

Title: Optimal time to sell a stock with a jump to default 

Abstract: We consider the problem of identifying the optimal time to sell a defaultable asset in the sense of minimizing the "prophet's drawdown" which is the ratio of the ultimate maximum (up to a random default time) and the value of the asset price at the moment of sale. We assume that default occurs at a constant rate, and that at the moment of default there is a random recovery value of $\rho(100)\%$. This problem is transformed to an optimal stopping problem, which we solve explicitly in the case that the asset price before default is modelled by a spectrally negative exponential Levy process. This is joint work with A. Mijiatovic.

Date: 6 November 2014

Speaker: Martin Schweizer, ETH Zurich

Time: 16:30-17:30

Place: Strand Campus, S-1.27 (1st basement, Strand Building)

Title: A new approach for stochastic Fubini theorems

Abstract: We prove a new stochastic Fubini theorem in a setting where we stochastically integrate a mixture of parametrised integrands, with the mixture taken with respect to a stochastic kernel instead of a fixed measure on the parameter space. To that end, we introduce a notion of measure-valued stochastic integration with respect to a multidimensional semimartingale. As an application, we show how one can handle a class of quite general stochastic Volterra semimartingales. The original question for this work came from a problem in mathematical finance, and we also briefly comment on that. The talk is based on joint work with Tahir Choulli (University of Alberta, Edmonton).

Speaker: Knut Aase, Norwegian School of Economics

Time: 17:45-18:45

Place: Strand Campus, S-1.27 (1st basement, Strand Building)

Title: Beyond the local mean-variance analysis in dynamic economics: Recursive utility etc 

Abstract: I derive the equilibrium interest rate and risk premiums using recursive utility for jump-diffusions. Compared to to the continuous version, including jumps allows for a separate risk aversion related to jump size risk in addition to risk aversion related to the continuous part. We consider the version of recursive utility which gives the most unambiguous separation of risk preference from time substitution, and use the stochastic maximum principle to analyze the model. This method uses forward/backward stochastic differential equations. The model with jumps is shown to have a potential to give better explanation of empirical regularities than the recursive models based on merely continuous dynamics. Deviations from normality in the conventional model are also treated.

Date: 20 November 2014

Speaker: Gordan Zitkovic, University of Texas at Austin

Time: 16:30-17:30

Place: Strand Campus, S-1.27 (1st basement, Strand Building)

Title: On the dynamic programming principle for problems posed over martingale measures

Abstract: After an overview of the existing results on dynamic programming in continuous time, a simple abstract framework in which it holds will be described, and then used to analyze a class of problems posed over the "set of martingale measures". As an application, the super-replication and utility-maximization problems in a rather general family of incomplete Markovian financial market models will be treated.

Speaker: Sergio Pulido, Swiss Finance Institute

Time: 17:45-18:45

Place: Strand Campus, S-1.27 (1st basement, Strand Building)

Title: Existence and uniqueness results for multi-dimensional quadratic BSDEs arising from a price impact model with exponential utility

Abstract: In this work we study multi-dimensional systems of quadratic BSDEs arising from a price impact model where an influential investor trades illiquid assets with a representative market maker with exponential preferences. The impact of the strategy of the investor on the prices of the illiquid assets is derived endogenously through an equilibrium mechanism. We show that a relationship exists between this equilibrium mechanism and a multi-dimensional system of quadratic BSDEs. We also specify conditions on the parameters of the model that guarantee that the system of BSDEs has a unique solution, which corresponds to a family of unique equilibrium prices for the illiquid assets. The proof relies on estimates that exploit the structure of the equilibrium problem. Finally, we provide examples of parameters for which the corresponding system of BSDEs in not well-posed.

Joint work with Dmitry Kramkov.

Date: 4 December 2014

Speaker: Ragnar Norberg, University Lyon 1

Time: 16:30-17:30

Place: Strand Campus, S-1.27 (1st basement, Strand Building)

Title: On Marked Point Processes: Modelling, Stochastic Calculus, and Computational Issues

Abstract: The talk starts with a friendly introduction to marked point processes and their associated counting processes and martingales. Then it proceeds to three distinct, still intertwined, aspects of the theory: Modelling is a matter of specifying the intensities, which are the fundamental model entities with a clear interpretation as instantaneous transition probabilities; Prediction is a matter of calculating conditional expected values of functionals of the process, which involves stochastic calculus (can be made simple); Computation is a matter of solving Ordinary or Partial Integral-Differential Equations, looking for shortcuts (ODEs replacing PDEs) and looking out for pitfalls (non-smoothness points that cannot be detected by inspection of the equations). The unifying powers and the versatility of the model framework are demonstrated with examples from risk theory, life insurance, and non-life insurance.

Speaker: Michael Kupper, University of Konstanz

Time: 17:45-18:45

Place: Strand Campus, S-1.27 (1st basement, Strand Building)

Title: Robust Pricing Dualities

Abstract: We focus on representation results for monotone convex functionals with countably additive measures. As an application we consider a continuous-time financial market model under a family of probability measures and show that there exists no free lunch with disappearing risk if and only if there exists an equivalent family of martingale measures. Moreover, we discuss a generalized version of the transport duality with applications to model-free pricing. The talk is based on joint works with Patrick Cheridito and Ludovic Tangpi.

Date: 11 December 2014

Speaker: Peter Imkeller, Humboldt University Berlin

Time: 16:30-17:30

Place: Strand Campus, S-1.27 (1st basement, Strand Building)

Title: Cross hedging, (F)BSDE of quadratic growth and convex duality

Abstract: A financial market model is considered on which agents (e.g. insurers) are subject to an exogenous financial risk, which they trade by issuing a risk bond. They are able to invest in a market asset correlated with the exogenous risk. We investigate their utility maximization problem, and calculate bond prices using utility indifference. In the case of exponential utility, this hedging concept is interpreted by means of martingale optimality, and solved - even for non-convex constraints - with BSDE with drivers of quadratic growth. For more general utility functions defined on the whole or nonnegative real linewe show that if an optimal strategy exists then it is given in terms of the solution (X; Y;Z) of a fully coupled FBSDE. Conversely if the FBSDE admits a solution (X; Y;Z) then an optimal strategy can be obtained.

On a general stochastic basis, and with liability 0, we finally combine this FBSDE approach with the duality approach by Kramkov-Schachermayer who provide an abstract existence and uniqueness result for the optimal hedging strategy. Under some regularity conditions on the utility functions we associate to their solution a constructive one given by a numerically accessible FBSDE system describing the optimal investment process as the forward component, and a functional of the dual optimizer as the backward one. This is joint work with U.Horst, Y. Hu, V. Nzengang, A. Reveillac, and J. Zhang.

Speaker: Dylan PossamaïUniversité Paris Dauphine

Time: 17:45-18:45

Place: Strand Campus, S-1.27 (1st basement, Strand Building)

Title: BSDEs, existence of densities and Malliavin calculus

Abstract: In recent years the field of Backward Stochastic Differential Equations (BSDEs) has been a subject of growing interest in stochastic calculus as these equations naturally arise in stochastic control problems in Finance, and as they provide Feynman-Kac type formulae for semi-linear PDEs. Since it is not generally possible to provide an explicit solution to these equations, one of the main issues especially regarding the applications is to provide a numerical analysis for the solution of a BSDE. This calls for a deep understanding of the regularity of the solution processes Y and Z. Here, we focus on the marginal laws of the random variables Yt, Zt at a given time t in (0,T). More precisely, we are interested in providing sufficient conditions ensuring the existence of a density (with respect to the Lebesgue measure) for these marginals on the one hand, and in deriving some estimates on these densities on the other hand. This type of information on the solution is of theoretical and of practical interest since the description of the tails of the (possible) density of Zt would provide more accurate estimates on the convergence rates of numerical schemes for quadratic growth BSDEs. This issue has been pretty few studied in the literature, since up to our knowledge only references [2, 1] address this question. The first results about this problem have been derived in [2], where the authors provide existence of densities for the marginals of the Y component only and when the driver h is Lipschitz continuous in (y,z), and some smoothness properties of this density. Concerning the Z component, much less is known since existence of a density for Z has been established in [1] only under the condition that the driver is linear in z. We revisit and extend the results of [2, 1] by providing sufficient conditions for the existence of densities for the marginal laws of the solution Yt,Zt (with t an arbitrary time in (0,T)) of a qgBSDE with a terminal condition ξ in (1) given as a deterministic mapping of the value at time T of the solution to a one- dimensional SDE, together with estimates on these densities. En route to these results, we provide new conditions for the Malliavin differentiability of solutions of Lipschitz or quadratic BSDEs. These results rely on the interpretation of the Malliavin derivative as a Gâteaux derivative in the directions of the Cameron-Martin space. Incidentally, we provide a new formulation for the characterization of the Malliavin-Sobolev type spaces D1,p.

The talk is based on joint works with Peter Imkeller, Thibaut Mastrollia and Anthony Reveillac.

2013-14 seminar series

The London Mathematical Finance Seminar is a joint seminar series organised by Birkbeck College, Brunel University, Cass Business School, King's College, LSE and UCL. The seminar series is hosted by one institute in each academic term.

All are welcome to attend. No registeration is needed.

3 October 2013

Speaker: Mike Tehranchi
Cambridge University

Title: An HJM approach to equity derivatives

There has been recent interest in applying the Heath-Jarrow-Morton interest rate framework to other areas of financial modelling. Unfortunately, there are serious technical challenges in implementing the approach for modelling the dynamics of the implied volatility surface of a given stock. We provide a partial solution to these difficulties by giving an existence result for associated HJM equation for the evolution of symmetric surfaces. The proof relies on a suitable change of parametrisation of the surface.

17 October 2013

Speaker: Mark Davis
Imperial College London

Title: Foundations of Probability Forecasting and Risk Management

Recently there has been renewed debate about the relative merits of VaR and CVaR as measures of financial risk. VaR is not coherent and does not qantify the risk beyond VaR, while CVaR shows some computational instabilities and is not "elicitable" (Gneiting 2010, Zwiebel 2013).

It is argued in this talk that such questions are best addressed from the point of view of probability forecasting or Dawid's "prequential statistics". We introduce a concept of "consistency" of a risk measure, which is close to Dawid's "strong prequential principle", and show that VaR indeed has special properties not shared by any other risk measure.

Speaker: Gechun Liang
Kings College London

Title: Optimal Switching at Poisson Random Intervention Times

In this talk, we consider a class of optimal switching problems, where the player is allowed to switch at a sequence of exogenous Poisson arrival times, and the underlying switching system is governed by an infinite horizon backward stochastic differential equation system. The value function and the optimal switching strategy are characterized by the solution of the underlying switching system. In a Markovian setting, we give a complete description of the structure of switching regions by means of the comparison principle.

31 October 2013

Speaker: Stephane Loisel

Université Lyon 1

Title: Ruin probability for some particular correlated claims, for worsening risks, and risks with infinite mean

We first give explicit formulas for the infinite time ruin probability for some particular correlated claim amonts or interarrival times. We then investigate asymptotics of ruin probabilities when claim distribution is worsening over time, due to phenomena like sectorial inflation or global warming. We end up with some results in the case where claim amounts have infinite mean.

Speaker: Jocelyne Bion-Nadal

Ecole Polytechnique

Title: Martingale problem for path dependent diusion processes application to robust pricing

Diffusion processes are characterized by their generator. In this talk I present the study of the martingale problem for path dependent generators with possibly a jump term. I introduce a new topological point of view for progressive functions on the canonical space of cadlag paths. The existence and uniqueness of solutions to the martingale problem is proved under the asumption that the coecients of the diusion are progressive functions with some continuity properties. This result generalizes to the path dependent case the Stroock's results for diusions with Levy generators.

The nancial market information is usually compatible with many classes of models. This leads to the problem of robust pricing under a possibly non dominated set of probability measures on the space of cadlag paths. I propose the construction of a robust time consistent dynamic pricing procedure making use of the martingale problem approach.

14 November 2013

Speaker: Andrea Pascucci

University of Bologna

Title: Approximate Implied vol for any local-stochastic vol model

Abstract: We consider an asset whose risk-neutral dynamics is described by a general local-stochastic volatility model. In this setting, we derive a family of asymptotic expansions for the transition density of the underlying as well as for European-style option prices and for implied volatilities. Our expansions are numerically efficient. Approximate transition densities and implied volatilities are explicit; they do not require any special functions nor do they require numerical integration. Approximate option prices require only a Normal CDF (as is the case of the Black-Scholes setting). Additionally, we establish rigorous error bounds for our transition density expansion. To illustrate the accuracy and versatility of our implied volatility expansion, we implement this expansion under different model dynamics: CEV local volatility, quadratic local volatility, Heston stochastic volatility and 3/2 stochastic volatility.

Our implied volatility expansion is found to perform favorably compared to other well-known expansions for these models.

Speaker: Mario Wuthrich

Eidgenössische Technische Hochschule Zürich

Title: From Ruin Theory to Solvency in Non-Life Insurance

Abstract: We start from ruin theory considerations in the classical Cramer-Lundberg process. These considerations will be modified step by step so that we arrive at today's modern solvency assessments for non-life insurance companies. These modifications include discussions about time horizons, risk measures, claims development processes, financial returns and valuation of insurance liabilities.

28 November 2013

Speaker: Antonis Papapantoleon

Technische Universität Berlin

Title: Affine LIBOR models with multiple curves: theory, examples and calibration

Abstract: In this talk, we present an extension of the LIBOR market model with stochastic basis spreads, in the spirit of the affine LIBOR models. This multiple-curve model satisfies the main no-arbitrage and market requirements (such as nonnegative LIBOR-OIS spreads) by construction. The use of multidimensional affine processes as driving motions ensures the analytical tractability of the model. We provide pricing formulas for caps, swaptions and basis swaptions and discuss an efficient numerical implementation. Furthermore, the connection between the affine LIBOR setup and the 'classical' LIBOR market models is clarified. We present also some new examples of affine processes on $\mathbb{R}^2_+$ which admit explicit solutions of the Riccati equations. We conclude this talk by presenting calibration results to market data. This is joint work with Z. Grbac, J. Schoenmakers and D. Skovmand.

Speaker: Damir Filipovic

École Polytechnique Fédérale de Lausanne

Title: Linear-Rational Term Structure Models

Abstract: We introduce the class of linear-rational term structure models, where the state price density is modeled such that bond prices become linear-rational functions of the current state. This class is highly tractable with several distinct advantages: i) ensures non-negative interest rates, ii) easily accommodates unspanned factors affecting volatility and risk premia, and iii) admits analytical solutions to swaptions. For comparison, affine term structure models can match either i) or ii), but not both simultaneously, and never iii). A parsimonious specification of the model with three term structure factors and one, or possibly two, unspanned factors has a very good fit to both interest rate swaps and swaptions since 1997. In particular, the model captures well the dynamics of the term structure and volatility during the recent period of near-zero interest rates.

12 December 2013

Speaker: Riccardo Rebonato

Title: Affine Models for the Buy Side: Another Look at Convexity, Risk Premia and Reversion Levels

Abstract: There have been exciting new developments in affine modelling, which have pursued the increasingly converging paths of using principal components as mean-reverting factors, and imputing risk premia from the latter. These novel approaches offer exciting avenues, but also open up unexpected problems. The talk tries to explain what can and what cannot be done with an affine treatment of principal components, and highlights some unexpected 'impossibilities'. The risk premium beast remains elusive...

16 January 2014

Speaker: Bernt Oksendal

University of Oslo

Title: Model Uncertainty and Robust Duality in Finance

Abstract: A celebrated financial application of convex duality theory gives an explicit relation between the following two quantities:

(i) The optimal terminal wealth X*(T):= X_{\phi*}{T} of the classical problem to maximise the expected U-utility of the terminal wealth X_{\phi}{T} generated by admissible \phi(t); 0\leq t\leq T in a market with the risky asset price process modlled as a semimartingale.

(ii) The optimal scenario dQ*/dP of the dual problem to minimise the expected V-value of dQ/dP over a family of equivalent locl martingale measures Q.

Here V is the convex dual function of the concave function U.

1) In the first part of this talk we consider markets modelled by Ito-Levy processes, and we present a new approach to the above result in this setting, based on the maximum principle in stochstic control theory. An advantage with our approach is that it also gives an explicit relation between the optimal portfolio \phi* and the optimal scenario Q*, in terms of backward stochastic differential equations. This can be used to obtain a general formula for the optimal portfolio \phi*(t) by means of the Malliavin derivative.

2) In the second part we extend our study to a robust portfolio problem and its dual. More specifically, we study the portfolio problem and its dual under model uncertainty, and we prove a corresponding duality equivalence in that setting. Our approach allows us to obtain explicit relations between the solutions of the robust primal and robust dual problem.

We illustrate the results with explicit examples.

The presentation is based on joint work with Agnes Sulem, INRIA-Rocquencourt, France.

30 January 2014

Speaker: Julien Hok


Title: Forward implied volatility expansion in time-dependent local volatility models

Abstract: We introduce an analytical approximation to efficiently price forward start options on equity in time-dependent local volatility models as the forward start date, the maturity or the volatility coefficient are small. We use a conditional argument to represent the price as an expectation of a Black-Scholes formula computed with a stochastic implied volatility depending on the value of the equity at the forward date. Then we perform a volatility expansion to derive an analytical approximation of the forward implied volatility with a precise error estimate. We also illustrate the accuracy of the formula with some numerical experiment.


Speaker: Luca Capriotti
Credit Suisse

Title: Real time counterparty credit risk management with adjoint algorithmic differentiation (AAD)

Abstract: One the most active areas of risk management today is counterparty credit risk management (CCRM). Managing counterparty risk is particularly challenging because it requires the simultaneous evaluation of all the trades facing a given counterparty. For multi-asset portfolios this typically with extradordinary computational challenges.

We show how Adjoint Algorithm Differentiation (AAD) can be used to reduce the computational cost by hundreds of times. As a result, AAD allows one to perform in minutes risk runs that would take otherwise several hours or could not even be performed overnight without large parallel computers. AAD makes therefore possible risk time risk management in Monte Carlo, allowing investment firms to hedge their positions more effectively, actively manage their capital allocation, reduce their infrastructure costs, and ultimately attract more business.

13 February 2014

Speaker: Pierre Collin-Dufresne

École Polytechnique Fédérale de Lausanne

Title: Insider trading, stochastic liquidity and equilibrium prices

Abstract: We extend Kyle's (1985) model of insider trading to the case where liquidity provided by noise traders follows a general stochastic process. Even though the level of noise trading volatility is observable, in equilibrium, measured price impact is stochastic. If noise trading volatility is mean-reverting, then the equilibrium price follows a multivariate stochastic volatility 'bridge' process. More private information is recealed when volatility is higher. This is because insiders choose to optimally wait to trade more aggressively when noise trading volatility is higher. In equilibrium, market makers anticipate this, and adjust prices accordingly. In time series, insiders trade more aggressively, when measured price impact is lower. Therefore, aggregate execution costs to uninformed traders can be higher when price impact is lower.

The paper can be found here.

Speaker: Yan Dolinsky

Hebrew University

Title: Robust hedging with proptional transaction

Abstract: Duality for robust hedging with proportional transaction costs of path dependent European options is obtained in a discrete time financial market with one risky asset. Investor's portfolio consists of a dynamically traded stock and a static position in vanilla options which can be exercised at maturity. Trading of both the options and the stock are subject to proportional transaction costs. The main theorem is duality between hedging and a Monge-Kantorovich type optimization problem. In this dual transport problem the optimization is over all the probability measures which satisfy an approximate martingale condition realted to consistent price systems in addition to an approximate marginal constraints. (Joint work with Mete Soner)

27 February 2014

Speaker: Anis Matoussi
University of Maine

Title: American and game options under uncertainty via Reflected second-order BSDEs

Abstract: We study the existence and uniqueness of second-order reflected 2BSDEs with one and two obstacles. For the later one, under some regularity assumptions on one of the barriers, we provide a complete wellposedness theory for doubly reflected second-order BSDEs. We also show that tjese pbjects are related to non-standard optimal stopping games, thus generalizing the connection between DRBSDEs and Dynkin games first proved by Cvitanic and Karatzas (1996). More precisely, we show that the second order DRBSDEs provide solutions of what we call uncertain Dynkin games that they also allow us to obtain super and subhedging prices for American game options (also called Israeli options) in financial markets with volatility uncertainty.

This is based on several joint work with D. Possamai, C. Zhou, and L. Piozin.

Speaker: Monique Jeanblanc

Universite D'Evry

Title: Arbitrages in a progressive enlargment of filtration

Abstract: In a first part, we present some models where the no arbitrage condition in the reference filtration implies that there are no arbitrages in the progressively enlarged filtration. Then, we study the case of honest times. Under the hypothesis that the financial market is complete in the reference filtration, we show that there exists arbitrages in the enlarged filtration, before and after the random time used to enlarged the filtration.

In a third part, we pay attention to arbitrages to the first kind. We give criteria such that this condition remains valud in the enlarged filtration (before and after the random time), and we give some examples corresponding to logarithm wealth optimization.

Joint work with A. Aksamit, T. Choulli, J. Deng.

13 March 2014

Speaker: Giulia Iori

City University

Title: The Impact of Reduced Pre-Trade Transparency Regimes on Market Quality

Abstract: The paper studies the effects of pre-trade quote transparency on spread, price discovery and liquidity in an artificial limit order market with heterogeneous trading rules. Our numerical experiments suggest that full quote transparency incurs to substantial transaction costs to traders and dampens trading activity in an order-driven market. Ecogenous restriction of displayed depth, up to several best quotes, does not benefit market performance. On the contrary, endogenous restriction of displayed quote depth, by means of iceberg orders, improved market quality in multiple dimensions: it alleviates the problem of adverse selection to patient limit order traders, relieves average transaction costs, maintains higher liquidity and moderate olatility, balances the limit order book and enhances price discovery.

Speaker: Frank Riedel

Bielefeld University

Title: Finance under Knightian Uncertainty

Abstract: We develop some basic results of finance under Knightian, or model uncertainty.

In a first step, we investigate how one can formulate the basic hedging and asset pricing results without working with a probability space. In this case, topological considerations play a role.

In a second step, we consider the new framework of stochastic calculus based on Peng's theory of uncertainty. We consider (super)hedging prices and duality results and present some fist results on financial equilibria.

We will also solve the usual Merton portfolio problem when interst rate and volatility are ambiguous. A surprising result says that the investor optimally puts all wealth into stocks when interest rate ambiguity is stoo large.

References: 1 and 2

27 March 2014

Speaker: Christa Cuchiero

Vienna University of Technology

Title: A convergence result for the Emery topology and insights in the proof of the fundamental theorem of asset pricing

Abstract: here

Speaker: Torsten Schoeneborn
Deutsche Bank

Title: Adaptive basket liquidation

Abstract: We consider the infinite time-horizon optimal basket portfolio liquidation problem fr a von Neumann-Morgenstern investor in a multi-asset extension of the liquidity model of Almgren (2003) with cross-asset impact. Using a stochastic control approach, we establish a "separation theorem'': he sequence of portfolios held during an optimal liquidation depends only on the (co-)variance and (cross-sset) market impact of the assets, while the speed with which these portfolios are attained depends only on the utility function of the trader. We derive partial differential equations for both the sequence of attained portfolios and the trading speed.

22 May 2014

Speaker: Francois Delarue

Universite Nice

Title: Large population stochastic control with a common noise

Abstract: We discuss the optimal control of mean-field interacting financial agents subjected to the influence of two noises: a noise that is specific to each agent and a noise that is common to all of them. Assuming that the agents obey similar dynamics, we investigate asymptotic equilibriums inside the population when the number of players tends to the infinity. We show that asymptotic McKean-Vlasov type. We also show that the decoupling field o this forward-backward system satisfies a 'master equation' according to the terminology introduced by Lasry and Lions in the theory of mean-field games.

Speaker: Luca Capriotti
Credit Suisse

Title: Real time counterparty credit risk management with adjoint algorithmic differentiation (AAD)

Abstract: One the most active areas of risk management today is counterparty credit risk management (CCRM). Managing counterparty risk is particularly challenging because it requires the simultaneous evaluation of all the trades facing a given counterparty. For multi-asset portfolios this typically with extradordinary computational challenges.

We show how Adjoint Algorithm Differentiation (AAD) can be used to reduce the computational cost by hundreds of times. As a result, AAD allows one to perform in minutes risk runs that would take otherwise several hours or could not even be performed overnight without large parallel computers. AAD makes therefore possible risk time risk management in Monte Carlo, allowing investment firms to hedge their positions more effectively, actively manage their capital allocation, reduce their infrastructure costs, and ultimately attract more business.

29 May 2014

Speaker: Min Dai

National University of Singapore

Title: Asymptotics for Merton problem with capital gain taxes and small interest rate

Abstract: We consider the continuous time optimal investment and consumption decision of a constant relative risk aversion investor who faces capital gain taxes. We provide asymptotic expansions with small interest rate. Our expansions offer a good approximation of the optimal buy and sell boundaries for small interest rate. Moreover, we obtain an estimate of the equivalent wealth loss due to capital gain taxes. In addition, we present an estimate of the optimal weight in the risky asset after realizing capital gain losses. Numerical results are presented to demonstrate our theoretical analysis. This work is jointly with Xinfu Chen.

2012-13 seminar series

25 October 2012

Speaker: Nizar Touzi
Centre de Mathématiques Appliquées, Ecole Polytechnique

Title: Viscosity solutions of fully nonlinear part-dependent PDEs 

Abstract: We propose a notion of viscosity solutions for path dependent fully nonlinear parabolic PDEs. This can be viewed as an alternative approach to backward stochastic differential equations and their second order extension. One typical example is the path dependent HJB equations, which can also be viewed as viscosity solutions of second order Backward SDEs and G-martingales. The definition is based on a nonlinear optimal stopping problem, and is consistent with the notion of classical solution in the sense of Dupire's functional It\^o calculus. We prove the existence, uniqueness, stability, and comparison principle for the viscosity solutions.

Speaker: Alexander Schied
Department of Mathematics, University of Mannheim

Title: Trading under transient price impact 

Abstract: Based on an idealized model of a limit order book with resilience, Obizhaeva & Wang (2005) were the first to analyse optimal portfolio liquidation trajectories under transient price impact. Their original model has been generalised in several ways, e.g., so as to include nonlinear price impact, non-exponential resilience, multiple assets, or additional drift. In this talk, we will review some of these extensions and discuss the optimisation problems arising in the corresponding portfolio liquidation problems. Particular emphasis will be given to the role played by a drift in asset prices.

1 November 2012

Speaker: Ying Hu
Universite de Rennes 1, Institut de recherche mathematique de Rennes

Title: Ergodic BSDEs and Applications

Abstract: In this talk, we first introduce the notion of ergodic BSDE which arises naturally in the study of ergodic control.

The ergodic BSDE is a class of infinite-horizon BSDEs where the unknown is the triple $(Y, Z, \lambda)$: $Y, Z$ are adapted processes and $\lambda$ is a real number. We review the existence and uniqueness result for ergodic BSDE under strict dissipative assumption.

Then we study ergodic BSDEs under weak dissipative assumptions. We show the existence and uniqueness of solution to the ergodic BSDE by use of uniform coupling estimates for perturbed forward stochastic differential equations. Furthermore, we give some recent results on ergodic BSDEs with quadratic generators and ergodic BSDEs driven by Markov chains.

Finally, applications are given to the optimal ergodic control of stochastic differential equations to illustrate our results. We give also connections with ergodic PDEs.

Speaker: Chris Rogers

University of Cambridge, Quantitative Finance Group, Statistical Laboratory

Title: Extremal martingales

Abstract: Availability of market prices of call options of all strikes determines the risk neutral distribution of the underlying asset at the terminal time. Finding the maximum and minimum price of various derivatives whose prices depend on the maximal value and the terminal value (such as barrier options) has been studied in the last 15 years or so by Hobson, Cox, Obloj, Brown, and others, and some quite complete results are known. This talk takes as its starting point some older work characterizing the possible joint laws of the maximum and terminal value of a martingale; this converts the problem of finding the extremal martingale into a linear programming problem, an observation which allows effective numerical solution. More recent work with Moritz Duembgen characterizes the possible joint distributions of the maximum, minimum, and terminal value of a continuous martingale.

15 November 2012

Speaker: Nick Bingham
Imperial College London, Department of Mathematics

The Worshipful Company of Actuaries annual lecture


Title: Risk for actuaries and risk for everyone


Speaker: Juan Carlos Pardo
Centro de Investigacion en Matematicas

Title: Occupation times for refracted Levy Processes


29 November 2012

Speaker: Michael Monoyios
University of Oxford, Department of Mathematics

Title: Malliavin calculus method for asymptotic expansion of dual control problems

Abstract: We develop a technique based on Malliavin calculus ideas, for asymptotic expansion of dual control problems arising in connection with exponential indifference valuation of claims, and with minimisation of relative entropy, in incomplete markets. The problems involve optimisation of functional in which the control features quadratically, while in the state dynamics it appears as a drift perturbation to Brownian paths on Wiener space. This drift is interpreted as a measure change using the Girsanov theorem, leading to a form of the integration by parts formula in which a directional derivative on Wiener space is computed. Applications to incimplete Ito process markets are given, in which indifference prices are approximated in the low risk aversion limit. We also give an application to identifying the minimal entropy martingale measure as a perturbation to the minimal martingale measure in stochastic volatility models.

13 December 2012

Speaker Hans Föllmer
Humboldt Universitat zu Berlin

Title: Shifting martingale measures and the birth of a bubble

Abstract: We study a flow in the space of equivalent martingale measures. This will allow us to capture the birth of a perceived bubble and to describe it as an initial submartingale which then turns into a supermartingale and falls back to its initial value zero. The talk will be based on joint work with F. Biagini and S. Nedelcu

Speaker: Michel Dacorogna

Title: Surviving the next crisis, a risk management perspective

Abstract: With the economic and financial crisis, the question of solvency has become increasingly discussed and challenged. This presentation addresses the current financial crisis, analyses its specific nature, its impact on the financial system and its consequences on the solvency requirements. It takes a fresh look at crises and their characteristics to draw lessons for risk management.

The pro-cyclicality of the current capital models for insurances is highlighted and its consequences on financial stability are discussed. It finally proposes to make the regulatory system more flexible to respond to future crises and suggests a way to do it without compromising the principles on which the whole valuation model is built.

31 January 2013

Speaker: David Hobson
University of Warwick

Title: Indivisible Asset Sales, Consumption and Undiversifiable Risks

Abstract: Consider an agent with a single unit of an indivisible asset to sell, the price of which fluctuates over time. The aim of the agent is to maximise utility of consumption over time. In addition to the indivisible asset the agent has outside wealth and she is free to invest this wealth on a financial market. When should the agent sell the indivisible asset? What should her investment and consumption strategies be, both before and after she sells the asset? We set up the problem as a stochastic control problem. The solution has some natural and expected features, but there are also some suprising consequences.

Speaker: Dilip Madan
University of Maryland at College Park

Title: Two Price Economies in Continuous Time

Abstract: Static and discrete time pricing operators for two price economies are ewviewed and then generalized to the continuous time setting of an underlying Hunt process. The continuous time operators define nonlinear partial integro-differential equations that are solved numerically for the three valuations of bid, ask and expectation. The operators emply concave distortions by inducing a probability into the infinitesimal generator of a Hunt process. This probability is then distorted. Two nonlinear operators based on different appraoches to truncating small jumps are developed and termed QV for quadratic variation and NL for normalized Levy. Examples illustrate the resulting valuations. A sample book of derivatives on a single underlier is employed to display the gap between the bid and ask values for the book and the sum of comparable values for the components of the book.

14 February 2013

Speaker: Kostas Kardaras

Title: A guide through market viability for frictionless markets

Abstract: In this talk, we elaborate on the notions of no-free-lunch that have proved essential in the theory of financial mathematics --- most notably, arbitage of the first kind. Focus will be given in most recent developments. The precise connections with the semimartingale property of asset-price processes, as well as existence of deflators, numeraires and pricing probabilities via use of Foellmer's exit measure are explained. Furthermore, the consequences that these notions have in the valuation of illquid assets in the market will be briefly explored.

Speaker: Giovanni Cesari

Title: CVA/FVA/RWA: A portfolio view to price derivatives

Abstract: Pricing and hedging derivatives is moving from using highly sophisticated models for single trades to a portfolio view, which enables firms to consider the cost of counterparty exposure, cost of collateral, and cost of funding.

In this talk, starting from the computation of counterparty credit exposure, we examine the interaction between CVA, DVA, and FVA, and suggest how to build a framework to compute these quantities consistently.

28 February 2013

Speaker: Jean Jacod
Universite Paris VI

Title: New efficient estimators for integrated volatility in the presence of non-summable jumps

Abstract: Estimation of the integrated volatility for Ito semimartingales which are discretely observed at n points is well understood, when the underlying process is continuous, or has summable jumps, and in this case it is possible to achieve the standard sqrt(n) convergence rate. When jumps are not summable the minimax rate becomes smaller. However, if one assumes that the small jumps are sufficiently close to those of a stable process (or a stochastic integral with respect to a stable process), we will show that it is possible to construct estimators with rate sqrt{n} again, and even variance-efficient under a kind of symmetry assumption.

This is a joint work with Viktor Todorov.

Speaker: Bryan Joseph


Title: Insurance - A Practical Use of Mathematics and Statistics

Abstract: The insurance industry has long relied on mathematics and statistics to define its business. Actuaries, as the financial engineers of this industry, has long been at the heart of this business. The talk is aimed at providing a practical perspective of an actuary and showing how mathematics is being applied in a number of different circumstances within the industry and how current developments are beinging new problems and requiring new or different solutions from practioners.

14 March 2013

Speaker: Fred Espen Benth
University of Oslo

Title: Modelling energy forward markets

Abstract: We analuse various approaches to model forward prices in energy markets. Empirical findings suggest a high degree of isionsyncratic risk between contracts at different matruities, pointing towards infinite-dimensional models for the price dynamics. We introduce a class of infinite-dimensional Levy processes based on subordination, and apply these in an HJM-approach to forward price modelling. Explicit representations of the spot price dynamics are classified. We also investigate a different pricing approach based on Ambit fields. Here, one is modelling the dynamics of forward prices directly rather than as the solution of some stochastic partial differential equation. Applications will be studied, including numerical simulation and optimal investments.

Speaker: Andrew Cairns
Heriot-Watt University

Title: Robust hedging of longevity risk

Abstract: We will begin with a brief introduction to longevity risk and the types of contract that might be used to hedge it including q-forwards and longevity swaps.

We consider situations where a pension plan has opted to hedge its longevity risk using an index-based longevity hedging instrument. The use of index-based hedges gives rise to basis risk, but benefits, potentially, from lower costs to the hedger and greater liquidity. We focus on quantification of optimal hedge ratios and hedge effectiveness and investigate how robust these quantities are relative to inclusion of recalibration risk, parameter uncertainty and Poisson risk. In contrast, single-instrument hedging strategies are found, in general, to lack robustness relative to the inclusion of recalibration risk at the future valuation date, although we also demonstrate that some hedging instruments are more robust than others. To address this problem, we develop multi-instrument hedging strategies that are robust relative to recalibration risk.

21 March 2013

Speaker: Andreas Kyprianou
University of Bath

Title: Censored stable processes

Abstract: We look at a general two-sided jumping strictly alpha-stable process where alpha is in (0,2). By censoring its path each time it enters the negative half line we show that the resulting process is a positive self-similar Markov process. Using Lamperti's transformation we uncover an underlying driving Levy process and, moreover, we are able to describe in surprisingly exlicit detail the Wiener-Hopf factorization of the latter. Using this Wiener-Hopf factorization together with a series of spatial path transformation, it is now possible to produce an explicit formula for the law of the original stable processes as it first ``enters" a finite interal, thereby generalizing a result of Blumenthal, Getoor and Ray fro symmetric stable processes from 1961.

This is joint work with Alex Watson(Bath) and JC Pardo(CIMAT).

27 March 2013

Speaker: Michail Anthropelos
University of Piraeus

Title: Agents' stategic behavior in optimal risk sharing

Abstract: We consider the market of n financial agents who aim to increase their utilities by efficiently sharing their random endowments. Given the endogenously derived optimal sharing rules, we address the situation where agents do not reveal their true endowments, but instead they report as endowments the random qantities that maximize their utilities when the sharing rules are applied. Under mean-variance preferences, it is shown that each agent should share only a fraction of his true endowment and report that he is exposed to some endowment he does not possess. Furthermore, if all agents follow similar strategic behavior, the market equilibrates at a Nash-type equilibrium which benefits the speculators and results in risk sharing inefficiency. This agents' strategic behavior, when applied to oligopoly markets of exogenously given financial securities, changes the effective market portfolio and implies a price pressure on the traded securities.

Speaker: Sara Biagini
Scuola Normale Superiore, Pisa

Title: Dynamic quasi-concave performance measures

Abstract: We define Conditional quasi concave Performance Measures (CPMs), on random variables bounded from below, to accommodate for additional information. Our notion encompasses a wide variety of cases, from conditional expected utility and certainty equivalent to conditional acceptability indexes. We provide the characterization of a CPM in terms of an induced family of conditional convex risk measures. In the case of indexes these risk measures are coherent. Then, Dynamic Performance Measures (DPMs) are introduced and the problem of time consistency is addresses. The definition of time consistency chosen here ensures that the positions which are considered good tomorrow are already considered good today. We prove the equivalence between time consistency for a DPM and weak acceptence consistency for the induced families of risk measures. Finally, we extend CPMs and DPMs to dividend processes.

Joint work with J. Bion-Nadal, Ecole Polytechnique and CNRS

9 May 2013

Speaker: Walter Schachermayer
University of Vienna

Title: Portfolio Optimisation under Transation Costs

Abstract: We give an overview of some old and some new results on portfolio optimiszation under transaction costs. The emphasis will be on an asymptotic point of view when proportional transaction costs tend to zero.

23 May 2013

Speaker: Stephane Villeneuve
Toulouse School of Economics

Title: Optimal liquidity management under partial information about the firm's profitability

Abstract:We revisit the classical problem of optimal dividend distribution by assuming that the profitability of the cash reserves process is not observable. This leads us to solve a defenerate bi-dimensional singular control problem where the two state variables are the cash reserves and the posteriori belief about the firm's profitability. We characterize the value function by means of viscosity solution and provide an explicit solution when the firm's profitability has a symmetric two points distribution.

Speaker: Jean-Philippe Bouchaud
Capital Fund Management

Title: Liquidity, market impact, HFT: the complex ecology of financial markets

Abstract: We will review recent empirical findings concerning the impact of trades on prices, which is related to bod-ask spreads at high frequencies, and to what we call "latent liquidity" on lower frequencies, for so-called "metaorders". We discuss in particular a) the relation between spreads and volatility and the profitability of market making strategies and b) the rather surprising square root impact law of metaorders. We will argue that financial markets are (and have always been) on the verge of instability. The role of High Frequency Trading in the complex ecology of financial markets will be addressed.

31 May 2013

Speaker: Scott Robertson
Carnegie Mellon University

Title: Static fund separation for long term investments

Abstract: In this talk we will prove a class of static fund separation theorems, valid for investors with a long horizon and constant relative risk aversion, and with stochastic investment opportunities. An optimal portfolio decomposes as a constant mix of a few preference-free funds, which are common to all investors. The weight in each fund is a constant that may depend on an investor's risk aversion, but not on the state variable, which changes over time. Vice versa, the composition of each fund may depend on the state, but not on the risk aversion, since a fund appears in the portfolios of different investors. We prove these results for two classes of models with a single state variable, and several assets with constant correlations with the state. In the linear class, the state is an Ornstein-Uhlenbeck process, risk premia are afine in the state, while volatilies and the interest rate are constant. In the square root class, the state follows a square root diffusion, expected returns and the interest rate are affine in the state, while volatilities are linear in the square root of state.

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London Mathematical Finance Group: 2016-17