Synopsis

Introduction to markets, assets, interest rates and present value; arbitrage and the law of one price: European call and put options, payoff diagrams; other option strategies. Wiener processes as models for asset price movements; informal treatment of Ito's formula and stochastic differential equations. Discussion of the connection with PDE's through the Feynman-Kac formula. Hedging and the Black-Scholes analysis, leading to the Black-Scholes partial differential equation for a derivative price. Explicit solution for call and put options through risk neutral pricing as well as the heat equation. Extensions to dividends paid on the asset and time-varying parameters. Forward and future contracts, options on them. American options as free boundary problems and linear complementarity problems. Simple exotic options. Weakly path-dependent options including barriers, lookbacks and Asians. Further course information and exercises etc can be found at o10 Mathematics of financial derivatives. Note that this is also an undergraduate course.

Reading List

• T Bjork, Arbitrage Theory in Continuous Time OUP, 1998

• P Wilmott, S D Howison,and J Dewynne, Mathematics of Financial Derivatives, CUP, 1995

• J Hull, Options Futures and Other Financial Derivative Products, Prentice Hall, 1999

• Eatwell et al (Eds.), The New Palgrave Finance, MacMillan,1998

  The second two are for background only.