Courses offered in Oct-Dec 2017

Courses offered 
in Oct-Dec 2017
MF23 Advanced Probability Theory

Lecturer: Dr. Luciano Campi, LSE
Time and dates:  Lectures at 10-12am, on September 27, October 04-11-18-25, November 8-15-22-29, December 6
Seminars at 12-13am, on October 2-9-16-23, November 6-13-20-27, December 4; extra slot at 14-15pm on November 6. 

Location: OLD.3.25 (Lectures), CLM.2.04 (Seminars), CLM.3.07 (extra-slot 14-15pm on Nov 6)
OLD.3.25 is in the Old Building, while CLM.2.04 and CLM.3.07 are in Clement House
The seminars will be run by Beatrice Acciaio.

Analysis and algebra at the level of a BSc in pure or applied mathematics and basic statistics and probability theory with stochastic processes. Knowledge of measure theory is not required as the course gives a self-contained introduction to this branch of analysis.

Course summary:
The course covers core topics in measure theoretic probability and modern stochastic calculus, thus laying a rigorous foundation for studies in statistics, actuarial science, financial mathematics, economics, and other areas where uncertainty is essential and needs to be described with advanced probability models. Emphasis is on probability theory as such rather than on special models occurring in its applications. Brief review of basic probability concepts in a measure theoretic setting: probability spaces, random variables, expected value, conditional probability and expectation, independence, Borel-Cantelli lemmas Construction of probability spaces with emphasis on stochastic processes. Operator methods in probability: generating functions, moment generating functions, Laplace transforms, and characteristic functions. Notions of convergence: convergence in probability and weak laws of large numbers, convergence almost surely and strong laws of large numbers, convergence of probability measures and central limit theorems. If time permits and depending on the interest of the students topics from stochastic calculus might be covered as well.

Indicative reading:
Williams, D. (1991): Probability with Martingales. Cambridge University Press;
Kallenberg, O. (2002). Foundations of modern probability. Springer;
Billingsley, P(2008). Probability and measure. John Wiley& Sons;
Jacod, J., & Protter, P. E. (2003). Probability essentials. Springer;
Dudley, R. M. (2002). Real analysis and probability (Vol. 74). Cambridge University Press
MF21 Advanced Derivative Pricing and Calibration via Quadrature

Lecturer: Dr. Marcello Minenna, CONSOB (The Italian Securities and Exchange Commission), Bocconi University (Milan)
Time and dates:   Wednesday 11th of October 12.15am to 3pm
Wednesday 25th of October 12.15am to 3pm
Wednesday 8th of November 12.15am to 3pm
Wednesday 22th of November 12.15am to 3pm
Wednesday 6th of December 12.15am to 3pm

Location: LSE will host the course all in OLD 4.10 (Old Building, Houghton St), except 22nd Nov in CLM 6.02 (Clement House, 99 Aldwych). 

Calculus, Measure Theory, Probability, Stochastic Calculus, Stochastic Differential Equations, Ordinary Differential Equations, Partial Differential Equations, Matlab programming.

Course summary:
In this course a considerable number of equity derivatives models is presented by implementing a unique standardized pricing approach. The first part is devoted to the development of a pricing representation - very general - that includes the major classes of equity derivatives models developed in literature (from Black-Scholes-Merton, CEV, local volatility to AJD and Pure Jump models). Usually these models are presented with heterogeneous techniques, notations and a plethora of various pricing representations; conversely, by starting from the simplest examples, the course bring back all the models in a uniform, formalized approach. In the second part this standardized analytical environment allows the beneficial deployment of powerful numerical techniques (i.e. adaptive quadrature schemes) that can solve in a flexible way the pricing and hedging problems regardless of the model’s theoretical complexity. The course aims to end up with the building of the code of an efficient, modular “all-purpose” pricing and calibration engine.

Indicative reading:
Notes distributed by the Lecturer
A guide to Quantitative Finance, Minenna M. (2005), Riskbooks
Option Pricing via Quadrature, Minenna M. (2008), Riskbooks

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