Title: SDE Models and Monte Carlo Simulations in Finance

Speaker: Professor Xuerong Mao FRSE, Royal Society Wolfson Research Merit Award Holder, 1969 Chair Professor of Statistics, Department of Mathematics and Statistics, University of Strathclyde, UK

Timetable: 3:30-5:30pm on 13-15 September

Venue: DB-A04 and Teams

Abstract: In this short course we will explain how the probability theory is naturally used to model the financial data and to price the European options. The well-known Cox-Ross-Rubinstein (CRR) model will first be introduced. We will then point out how the CRR model could be generalised via differential equations. We will explain why the ordinary differential equations (ODEs) are not good enough for modelling financial systems and they needs to be developed into stochastic differential equations (SDEs). We will introduce the definition of the Brownian motion and the It\^o stochastic calculus as well as their fundamental properties. We will then discuss the Nobel prize winning model, namely the Black-Scholes model and the corresponding partial differential equations (PDEs) for the European call and put options. More generalised SDE models in finance will be mentioned. The corresponding Monte Carlo simulations will be used to illustrate the theory.

Organiser: Dr Yongmei Cai, Assistant Professor in Applied Mathematics/Statistics