The principal aim of this course is to provide students with an appreciation and understanding of how the application of mathematics, particularly stochastic mathematics, to the field of finance may be used to illuminate this field and model its randomness, resulting in greater understanding and quantification of investment returns and security prices.

The principal aim of this course is to show how stochastic mathematics can be used for the pricing and risk management of option contracts, and complex contingent claims in general. The course aims to provide a clear understanding of the intuition behind derivatives pricing, how models are implemented, and how they are used and adapted in practice. Strengths and weaknesses of different models, e.g., Black–Scholes, interest rate models, stochastic volatility, are examined. Both the theory and the implementation of the industry-standard models are considered in detail. Pricing problems are approached using multiple techniques including the well-known PDE, Monte-Carlo and martingale approaches.

Students should have knowledge of stochastic processes, in particular Brownian Motion, geometric Brownian motion and the underlying stochastic differential equations. Moreover, students should be familiar with the Ito integral and the Ito formula. Please note that computer programming skills are required for all the cases, as these involve numerical calculations.

Joshi, M (2008) The Concepts and Practice of Mathematical Finance, 2nd ed, Cambridge University Press. ISBN: 978-0-521-51408-8

Students should have knowledge of stochastic processes, in particular Brownian motion, geometric Brownian motion and the underlying stochastic differential equations. Moreover, students should be familiar with the Ito integral and the Ito formula. Knowledge of the Girsanov transformation is helpful, but not required.