Courses offered in Oct-Dec 2017

Time and dates:
TBC

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.

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.

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

In this course a vast number of equity derivatives models is presented by implementing a standardized, uniform pricing approach. The first part is devoted to the development of a very general pricing representation 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). Generally these models are presented with heterogeneous techniques, notations and a plethora of various pricing representation; by starting from the simplest examples, the course bring back all the models in a uniform, formalized approach. In the second part the standardized analytical environment allows the regular 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.

Contact us

Administration Contact

lgs-fm@kcl.ac.uk

King's College London

Share by: