Dr Johannes Ruf

This course is available on the BSc in Business Mathematics and Statistics, BSc in Mathematics and Economics, BSc in Mathematics with Economics and BSc in Statistics with Finance. This course is available as an outside option to students on other programmes where regulations permit. This course is available with permission to General Course students.

MA313 Probability for Finance is required

Main mathematical ideas in the modelling of asset price evolution and the valuation of contingent claims (e.g., calls, puts); discrete methods will dominate. Introductory treatment of the Black-Scholes continuous-time model. This course introduces a range of mathematical concepts and techniques of modern finance. It considers discrete and continuous time models for the price dynamics of actively traded assets. It develops the basic principles of risk-neutral valuation of contingent claims, such as call and put options. The course contains some elements of stochastic analysis such as Brownian motion, stochastic integration, stochastic change of variable formula, change of probability measures. These analytic tools are used for the pricing of contingent claims in stochastic models of financial markets. Specific topics studied include: one-period and multi-period binomial tree models; the Black and Scholes model; self-financing replicating portfolios; martingales and conditional expectation; Itô calculus; risk-neutral valuation of call and put options in the absence of arbitrage; the Black and Scholes formula; option deltas, gammas, vegas, and other sensitivities.

22 hours of lectures and 10 hours of classes in the LT.

Written answers to set problems will be expected on a weekly basis.

Lecture notes will be provided. Background texts: T Bjork, Arbitrage Theory in Continuous Time, Oxford Finance, 2004; A Etheridge, A Course in Financial Calculus, CUP, 2002; M Baxter & A Rennie, Financial Calculus, CUP, 1996; P Wilmott, S Howison & J Dewynne, The Mathematics of Financial Derivatives, CUP, 1995; J Hull, Options, Futures and Other Derivatives, 6th edition, Prentice-Hall, 2005. D Lamberton & B Lapeyre, Introduction to stochastic calculus applied to finance, 2nd edition, Chapman & Hall, 2008. S E Shreve, Stochastic Calculus for Finance. Volume I: The Binomial Asset Pricing Model; Volume II: Continuous-Time Models. Springer, New York, 2004.

Exam (100%, duration: 2 hours) in the main exam period.