All modules are subject to availability each year and the department reserves the right to amend the module options.

1. Financial Mathematics I

(Dr M Tretyakov, Applied Mathematics, 15 credits (36 lectures), 1st semester)

This module together with the course “Financial Mathematics II” 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 II”. 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.

2. Principles of Finance

(Economics, 15 credits, 1st semester)

On completion of this module typical students should be able to: apply mathematical methods in finance; describe the main classes of financial assets; use mathematical and statistical methods to construct diversified equity portfolios; explain the nature of risk and risk-reduction in financial markets; describe attitudes to risk and explain how they influence portfolio choices and the market prices of assets; explain the concepts of equilibrium and arbitrage and use them to value securities; demonstrate an understanding of capital market efficiency and explain the significance of market efficiency for resource allocation.

3. Financial Systems and Institutions

(Prof. P. Demetriades, Economics, 15 credits, 1st semester)

On completion of this module typical students should be able to: discuss and evaluate the role of financial systems and institutions in modern economies; compare the relative effectiveness of different forms of financial regulation; use economic theory to assess the likely outcomes of different regulatory regimes; evaluate empirical evidence relating to the effectiveness of different financial systems.

4. C++ Programming and Advanced Algorithm Design

(Dr. N. Rahman, Computer Science, 15 credits, 1st semester)

This module teaches the basic principles of C++ programming and the design of algorithms on modern computer architectures. Students will be able to: understand the basic components of a C++ program including methods and attributes, the distinction between classes and instances, the structures required to write basic algorithms, algorithm analysis and design, modern computer architectures and memory hierarchies and some algorithms for scientific computing. Students, who have no or very little previous experience in C++, will be strongly encouraged to take this module.#

5. Applied Numerical Methods

(Prof. B. Leimkuhler, Applied Mathematics, 15 credits, 1st semester)

This course will introduce students in numerical approaches to scientific problems, including applications in engineering and physics. Various nonlinear differential equations will be introduced as simplified models for real-world systems, discretizations will be introduced, numerical methods will be developed for each application, and computer implementation (primarily in MatLab) will be considered. The idea is to help students learn how to tackle an application using numerical methods and to relate the computational results obtained to the model setting. Methods to be studied include iterative methods such as conjugate gradients for solving elliptic differential equations, stiff ordinary differential equation solvers for solving the heat equation. Finite difference schemes for differential equations and their stability. Appropriate linear algebra methods needed in the implementation of these schemes. Some theory will be presented but in limited detail.

6. Operational Research

(Dr. A. Iske, Applied Mathematics, 15 credits, 1st semester)

Dynamic programming and allocating investments. Markov chains and sequential decision making. Networks and graph theory. Linear programming and the simplex method. The theory of games. Scheduling problems. Input-output analysis. Forecasting.

7. Financial Mathematics II

(Applied Mathematics, 15 credits (36 lectures), 2ndt semester)

This module together with the course “Financial Mathematics I” will develop probabilistic tools to enable investors to value financial derivatives. It covers continuous time theory of financial derivatives pricing (Black-Merton-Scholes model, European and American options, stock and option prices, exotic options, swaps) based on stochastic calculus (Ito integrals, stochastic differential equations, Ito’s formula, Kolmogorov’s equations, Girsanov’s transformation). Interest rate modelling and fixed income securities. Financial risks. Greeks. Risk management. Basics of portfolio insurance risks.

8. Stochastic Numerics

(Dr. M. Tretyakov, Applied Mathematics, 15 credits, 2nd semester)

Principles of Monte Carlo technique. Generators of pseudo-random numbers. Mean-square and weak methods for numerical simulation of stochastic differential equations Application of weak methods to solving the Cauchy problem for linear parabolic partial differential equations, applications to models from Financial Mathematics. Variance reduction techniques (control variates, importance sampling). Practical homeworks. The course requires some preliminary knowledge of a programming language (e.g., C++ or MatLab).

9. Computational methods for PDEs

(Prof A. Gorban, Applied Mathematics, 15 credits, 2nd semester

Various numerical approaches (finite difference, finite element and boundary element methods) for solving PDEs of different types (elliptic, parabolic, hyperbolic). Mathematical formulation and implementation of the methods. Accuracy, reliability, efficiency and adaptivity. The methods will be discussed in the context of practical applications from the finance and engineering.

10. International Money and Finance

(Dr. M. Caglayan, Economics, 15 credits, 2nd semester)

On completion of this module typical students should be able to: apply theories and principles of monetary and macroeconomics to the analysis of problems in international finance; evaluate economic and econometric evidence relating to the working of international financial systems demonstrate the use of theory and empirical evidence in the development of policy advice.

12. Financial Econometrics

(Prof. W. Charemza, Economics, 15 credits, 2nd semester)

On completion of this module a typical student will be able to discuss central problems in financial econometrics and demonstrate the techniques used to analyse them. These will include: econometric analysis of market efficiency; interest and purchasing power parity; spot and forward exchange rates; ARCH and GARCH modelling of financial markets.

13. Corporate Finance

(Dr K Amess, Economics, 15 credits, 2nd semester)

On completion of this module typical students should be able to demonstrate: use of the theory of corporate finance; the analysis of problems in the acquisition and use of finance; the analysis of portfolio choice and behaviour; the implications of the capital asset pricing model; the use of capital budgeting; the application of theory to problems in takeovers, mergers and dividend policy.

14. Generlized Linear Methods

(Dr. S Paoli, Applied Mathematics, 15 credits, 1st semester)

This module aims to introduce the generalized linear model. It presents the methods of estimation of the linear model parameters and the methods of making inferences about these parameters through the calculation of confidence intervals and the use of hypothesis tests. In particular it is an aim of this course to impart understanding of how statistical models explain variation. The aim of covering the theory for the generalized linear model is to understand the extension of the theory to cover log-linear models for the analysis of counts and proportions and linear logistic regression models for binary data. Illustrations of how to use statistical software package GLIM to analyse data using the generalized linear model are given. Some applications to analysis of financial data are considered.