# The University of Edinburgh and Heriot-Watt University MSc Financial Mathematics

## Detailed Descriptions of Modules

Financial markets, 30 hours.  This module has two purposes: it will introduce students to the way financial markets and institutions function in practice, with particular emphasis on equities. The second part of the module will examine the structure of the fixed-income security markets and the methods by which they operate. An understanding of fixed-income securities (bonds) is crucial to understanding the valuation of all securities. This module will also examine, the main concepts used in calculating bond returns and evaluating bond portfolios.

Derivatives Markets, 15 hours.  The subject of derivatives is one that lies at the heart of the MSc. This half module will introduce students to the traded and over-the-counter derivatives markets. The main derivatives contracts will be described, and there will be discussion of the various practical issues connected with investment in the derivatives market.

Stochastic processes I, 35 hours. The mathematics needed in financial modelling is that of stochastic processes. This module will treat discrete stochastic processes, introducing simple financial models and showing how to price financial products in the discrete setting. It will also introduce Brownian motion and Stochastic Calculus.

Credit Risk Management, 30 hours. Credit risk is one of the key areas in modern financial mathematics. This module will introduce students to quantitative models for measuring and managing credit risk. It also aims to provide students with an understanding of the credit risk methodology used in the financial industry and the regulatory framework in which the credit risk models operate.

Financial Risk Management, 30 hours. This module will give students an introduction to the process of modelling financial risk based on the rigorous analysis of historical data. The course will look at a variety of tools to tackle problems involving financial data. Essential elements of the learning process are the computer labs where classroom theory is turned into practice.

Statistical methods, 30 hours.  Financial time series arise from stochastic processes. When it comes to the implementation of models it is essential to understand statistical techniques to estimate parameters and to fit models to real data. This module will cover a variety of statistical models as well as the concepts of estimation and hypothesis testing.

Simulation, 10 hours. There are many financial models where analytical solutions for derivative prices cannot be obtained. In these cases the only way to make progress is via simulation. This module will explain the basic ideas and methods of the simulation of behaviour of financial systems.

Stochastic processes II, 15 hours.  Stochastic Processes II will develop in detail the topic of stochastic calculus introduced in Stochastic Processes I, the key tool for the analysis of the continuous-time stochastic process framework in which financial models are set.

Modern portfolio theory, 30 hours.  This module will allow students to understand the theory of preference using utility theory and how this can be applied to selecting optimal portfolios. It will show how portfolio selection models can be extended to become pricing models and then focus on the basics of the CAPM and APT pricing models.

Derivative pricing and financial modelling, 30 hours.  The trade in derivatives has become much greater than trade in the underlying assets. This module will build on the stochastic processes courses to actually price and hedge a large number of financial products. It will deal with the plain vanilla options which fit into the Black-Scholes picture and then extend this to interest rate models and what happens when the Black-Scholes model breaks down.

Time series analysis, 15 hours.  This half-module will introduce students to the main concepts underlying the analysis of time series, and will discuss in detail some models which are frequently used for financial time series.

Financial econometrics, 15 hours.  Financial econometrics is the statistical modelling of financial data such as asset prices and returns. This module will begin with the analysis of univariate time series and then introduce the essentially econometric material in the context of multivariate financial time series.

Numerical techniques for partial differential equations, 15 hours.  Financial pricing problems can often be reduced to solving a partial differential equation. In this module numerical techniques for the solution of such equations will be introduced.

Mathematical programming, 15 hours.  Optimization techniques are used in many areas of finance. This module will discuss some of the theory and the practical implementation, introducing dynamic programming ideas.