MSc Financial Mathematics 2011/12

Module Information

TERM 1

Probability and Stochastic Processes (15 CATS)

Probability theory provides the language and the key technical concepts and tools for the study of financial mathematics. This course aims to introduce the basic ideas from probability which are of most relevance in finance, and to develop the machinery required to exploit these ideas. The course will begin with simple ideas such as events and random variables, but will progress rapidly to stochastic processes and to the study of the calculus for continuous time processes which are used in financial modelling.

Numerical Methods A (15 CATS)

This module aims to provide both a theoretical and a practical understanding of numerical methods in finance, in particular those related to simulations of stochastic processes. In addition the module will give an introduction into programming.
The syllabus will cover a range of topics including:-
Basics of linear models
GARCH and ARCH
CRR Model

Derivative Securities (15 CATS)

The course provides an introduction to derivative instruments. It aims to introduce various types of instruments traded in financial markets, the concepts of no-arbitrage pricing and hedging, and the mathematics of the discrete-time binomial models used to price derivatives.
The syllabus will cover a range of topics, including:-
Forwards and Futures - futures markets, forward pricing, hedging with futures
Fixed income and credit markets
Options
Binomial model for option
Option hedging

TERM 2

Continuous Time Finance for Interest Rate Models (15 CATS)

This module aims to build on knowledge from the term 1 prerequisite courses and to develop further an understanding of how stochastic calculus is used in continuous time finance. It also aims to develop an in-depth understanding of models used for interest rates. The syllabus will be split into three main areas; mathematical foundations, option pricing in continuous time and term structure models.
Topics likely to be covered include:-
Continuous Local Martingales
Girsanov’s Theorem for semi-martingales
Pricing via equivalent martingale measures, fundamental valuation formula, arbitrage and admissible strategies,
Completeness for the Black Scholes economy, pricing kernels
Implied volatility, market implied distributions, stochastic volatility and incomplete markets, Multicurrency Economy
Implementation of Hull-White

Financial Time Series (15 CATS)

The course aims to give practical experience in the use of specialized time series software by its use for class examples and projects. Students attending this module should be able to model and analyze financial time series data, and to extend and develop methodology as required; further, to understand and be able to critically evaluate times series developments and research results in the finance area.
Contents of the module will include:-
Prices and return, seasonality, statistical auto-dependency in financial series
Time series volatility, high-frequency financial data, directionality, forecasting; use of statistical analysis software
Linear models of time series, autoregressive and random walk models
Detailed developments and derivations of autoregressive models
Nonlinear modelling of financial time series: meaning of non-linearity, arch and models
Combining arma and arch models, GARCH models, financial illustrations using statistical software
Stochastic volatility models, interest rate models, and financial applications

Numerical Methods B (15 CATS)

This module aims to provide both a theoretical and a practical understanding of methods for solving partial differential equations by computer. It will stress the benefits and shortcoming of various methods for solving problems and teach the importance of program reliability testing. In particular, this module will impart a general computer competency (C++ programming language, project management, libraries and operating systems).
Building on the topics taught in Numerical Methods and Programming A, this module will include the following topics:-
Basics of parabolic PDEs: classification of linear and quasilinear second order PDEs and solution by separation of variables
Finite difference approximation of parabolic PDEs
Treatment of general boundary conditions. Nonlinearity: difficulties of nonlinear equations. Parabolic equations in higher dimensions. ADI scheme
Free boundary problem in option pricing and American options
Monte Carlo methods of pricing options