Dr Arne Lokka, COL 4.08

MA400 September Introductory Course (Financial Mathematics)

This course is primarily intended for students studying for the MSc Financial Mathematics, MSc Risk and Stochastics, MSc Management and Regulation of Risk, MSc Statistics (Financial Statistics), and MSc Statistics (Financial Statistics) (Research)

This course is also available to other suitably qualified students with the permission of the Degree Programme Director and the teacher responsible for the course.

This course is concerned with a mathematical development of the risk-neutral valuation theory. In the context of the binomial tree model for a risky asset, the course introduces the concepts of replication and martingale probability measures. The mathematics of the Black & Scholes methodology follow; in particular, the expression of European contingent claims as expectations with respect to the risk-neutral probability measure of the corresponding discounted payoffs, pricing formulae for European put and call options, and the Black & Scholes PDE are derived. A class of exotic options is then considered. In particular, pricing formulas for lookback and barrier options are derived using PDE techniques as well as the reflection property of the standard Brownian motion.  The course also introduces a model for foreign exchange markets and various foreign exchange options.

20 lectures, and 10 seminars in the MT.

Weekly exercises are set and form the basis of the classes.

N H Bingham and R Kiesel, Risk-Neutral Valuation, Springer; T Björk, Arbitrage Theory in Continuous Time, Oxford; P J Hunt and J Kennedy, Financial Derivatives in Theory and Practice, Wiley; D Lamberton and J Kennedy, Introduction to Stochastic Calculus Applied to Finance, Chapman & Hall; D. Lamberton and B. Lapeyre, Introduction to Stochastic Calculus Applied to Finance, Chapman & Hall/Crc Financial Mathematics Series, 2nd edition, 2007; S E Shreve, Stochastic Calculus for Finance: Continuous-time Models: vol. 2, Springer.

A two hour examination in the ST.