## The London Mathematical Finance Seminar Series

### 2013-14

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 - Imperial College London, Huxley Building (Lecture Theater 140)

16:00 - 17:00

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 (Bentham SB01 Seminar Room 3, University College London)

16:15 - 17:15

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.

17:30-18:30

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 (Mathematics Room 500, University College London)

16:15 - 17:15

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.

17:30 - 18:30

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 (Mathematics Room 500, University College London)

16:15 - 17:15

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.

17:30 - 18:30

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 (
Mathematics Room 500, University College London)

16:15 - 17:15

Speaker:
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.

17:30 - 18:30

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 (
Mathematics Room 500, University College London)

17:30 - 18:30

Speaker: Riccardo Rebonato
Pimco

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  (St Clement's S78, London School of Economics)

16:30 - 17:30

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  (St Clement's S78, London School of Economics)

16:30 - 17:30

Speaker: Julien Hok
Markit

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.

18:00 - 19:00 (Cancelled)

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  (St Clement's S78, London School of Economics)

16:30 - 17:30

Speaker:
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.

18:00 - 19:00

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  (St Clement's S78, London School of Economics)

16:30 - 17:30

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.

18:00 - 19:00

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  (St Clement's S78, London School of Economics)

16:30 - 17:30

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.

18:00 - 19:00

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 Clement House 3.02, London School of Economics  NEW ROOMNew Room

16:30 - 17:30

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

18:00 - 19:00

Speaker: Torsten Schoeneborn
Deutsche Bank

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

16:30 - 17:30

Speaker: Francois Delarue
Universite Nice

Title:

18:00 - 19:00

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

16:30 - 17:30

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.

18:00 - 19:00

Speaker:

Title: