Financial Mathematics 1

Module code: MA7071

Module co-ordinator: Sergey Utev

Module Outline

This module together with Financial Mathematics 2 will develop probabilistic tools to enable investors to value financial derivatives. Since there are no strict prerequisites on previous knowledge in probability and stochastics, the course contains mathematical preliminaries (probability space, random variables, distributions, independence, conditional expectation, random processes, simple random walks, Markovian property, martingales, stopping times).

It covers discrete time theory of option pricing (markets, forwards/futures, call and put European options, portfolios, hedging, arbitrage; drift, volatility; discrete Black-Scholes formula; American options). Stochastics will be taught together with financial models. The last part of this course starts building the background needed for continuous financial models considered mainly in Financial Mathematics 2. A transition from the binomial model of financial market to a continuous one. Wiener process and its properties. Stochastic differential equations and geometric Brownian motion.


  • 32 one-hour lectures
  • 14 one-hour seminars


  • Exam, two hours (100%)