Programme Outline
Students must take a total of eight taught modules, as specified in the list below. There is also an unassessed presessional module designed to help you review and consolidate material that is a prerequisite for the programme.
Modules with codes beginning MTH are taught by the School of Mathematical Sciences (SMS). These modules will cover the most important mathematical techniques used in quantitative finance, as well as topics in numerical methods and computing. Modules with codes beginning ECOM are taught by the School of Economics and Finance (SEF). These modules will cover the various financial instruments and markets, as well as other advanced topics in finance and economics. Modules are assessed by a mixture of interm assessment and final examinations, with examinations being held between late April and early June.
You will also undertake a project and dissertation during the summer, and this will be evaluated in September.
Successful completion of the MSc programme will result in the award of the MSc Mathematical Finance (possibly with Merit or with Distinction).
Please note that the precise contents of the programme may change from year to year, and so the information below is indicative only.
Taught Programme Structure (Full Time)
Semester A (Week 0)
SMS Presessional module: Financial Instruments; Probability and Calculus refreshers
Semester A
 MTH770P Computational Methods in Finance
 MTH771P Foundations of Mathematical Modelling in Finance
 Choose one from:
 Choose one from:
Semester B
 ECOM026 Financial Derivatives
 MTH772P Stochastic Calculus and BlackScholes Theory
 Choose one from:
 Choose one from:
Semester C
Module Outlines
MTH770P Computational Methods in Finance
This module will provide you with the necessary skills and techniques needed to investigate a variety of practical problems in mathematical finance. It is based on C++, the programming language of choice for many practitioners in the finance industry. You will learn about the basic concepts of the procedural part of C++ (inherited from the earlier C language), before being introduced to the fundamental ideas of objectoriented programming. The module is very ‘hands on’, with weekly sessions in the computer laboratory where you can put your theoretical knowledge into practice with a series of interesting and useful assignments.
Topics include:

Overview of technology in finance

Introduction to the Microsoft Visual Studio C++ development environment

Concepts in C++ such as data types, variables, arithmetic operations and arrays

Procedural programming, including branching statements, loops and functions

Introduction to objectoriented programming: Objects and classes

Examples from finance including bond pricing, histogramming historical price data, option pricing and risk management within the BlackScholes framework
MTH771P Foundations of Mathematical Modelling in Finance
This module introduces you to all of the fundamental concepts needed for your future studies in financial mathematics. After reviewing some key ideas from probability theory, we give an overview of some of the most important financial instruments, including shares, forward contracts and options. We next explain how derivative securities can be priced using the principle of no arbitrage. Various models for pricing options are then considered in detail, including the discretetime binomial model and the continuoustime BlackScholes model.
Topics include:

Review of key concepts in probability theory

Introduction to financial markets

Pricing derivatives by noarbitrage arguments

Discretetime option pricing models

Introduction to continuoustime stochastic processes and the BlackScholes model
MTH772P Stochastic Calculus and BlackScholes Theory
This module enables you to acquire a deeper understanding of the role of Ito stochastic calculus in mathematical finance, extending the material taught in MTH771P. We begin with some theoretical matters that build on Brownian motion, including concepts such as the Ito integral and Ito processes, and we discuss Ito’s lemma and its use in solving stochastic differential equations. We then turn to applications in finance, showing how the noarbitrage principle can be used to derive the famous BlackScholes formula for European call options. We further develop the concepts of riskneutrality and market completeness. Finally, we apply the methods of stochastic calculus to price different kinds of financial derivative, including exotic and Americanstyle options.
Topics include:

Overview of continuoustime stochastic processes, with a focus on Brownian motion

Construction of the Ito integral and Ito processes

Ito’s lemma, and its use in solving stochastic differential equations

Review of the BlackScholes formula for European call options, and the BS partial differential equation

Fundamental theorems of asset pricing

Constructing riskneutral measures in markets with one or many underlying assets

Pricing exotic and American options, term structure models, as time allows
MTH773P Advanced Computing in Finance
This module covers the advanced programming techniques in C++ that are widely used by professional software engineers and quantitative analysts & developers. The most important of these techniques is objectoriented programming, embracing the concepts of encapsulation, inheritance and polymorphism. We then use these techniques to price a wide range of financial derivatives numerically, using several different pricing models and numerical methods. On completion of this module, you will have acquired the key skills needed to apply for your first role as a junior ‘quant’ or software developer in a financial institution.
Topics include:

Advanced programming in C++: Classes and objects, dynamic memory allocation, templates, the C++ standard library, strings, container classes, smart pointers, design patterns

Stochastic models for asset prices (GBM, local volatility, stochastic volatility, jump diffusion)

Financial derivatives, including options on shares (e.g. European, American, digital, barrier, Asian, lookback, compound, chooser)

Implied volatility and the construction of the volatility smile

Fixed income and rates (bonds and yieldtomaturity, discount factor curve bootstrapping, stochastic interest rate models)

Numerical methods (interpolation, numerical quadrature, nonlinear solvers, binomial trees (CoxRossRubinstein), Monte Carlo methods, finitedifference methods for PDEs)
MTH774P Portfolio Theory & Risk Management
A very important general problem in finance is to balance investment risk and return. In this module you will acquire skills and techniques to apply modern risk measures and portfolio management tools. Mathematically this involves the maximization of the expectation of suitable utility functions which characterizes the optimum portfolio. You will learn about the theoretical background of optimization schemes and be able to implement them to solve practical investment problems.
MTH775P MSc Project and Dissertation
Each MSc Mathematical Finance student is required to complete a 60 credit project dissertation. A typical MSc project dissertation consists of about 30 wordprocessed pages (10,000 words), securely bound, covering a specific researchlevel topic in financial mathematics or economics, usually requiring the student to understand, explain and elaborate on results from one or more journal articles. An MSc project may also involve computation.
Some examples of possible project titles include:
 Analytical and numerical methods for pricing Asian options
 Jumpdiffusion models for equity prices
 Passport options
 Pricing and riskmanagement of CDOs and NTDs using Gaussian copula models
 Pricing interest rate derivatives with the LIBOR Market Model
 Stochastic volatility models for stock options
 Technical trading: trend and retracement
 The valuation of American options using Monte Carlo methods
 Variance Gamma models in finance
MTH777P Financial Programming
This module introduces you to some of the key technologies that are widely used for developing software applications in the financial markets and banking sectors. In particular, we focus on three programming environments/languages (Excel, VBA and C++) which are often used in conjunction to build complete trading and risk management systems. It is a highly practical module, focusing on current industry practice, and therefore you will be well equipped to apply for a programming role in a financial institution.
Topics include:

Overview of typical requirements for trading and risk management systems

Introduction to Microsoft Excel, and its use as a ‘front end’ for applications

Fundamentals of programming in VBA (Microsoft Visual Basic for Applications)

Manipulating Excel from VBA, the Excel object model

Review of C++, generation of dynamicallylinked libraries (DLLs) used as ‘back ends’ containing computation analytics

Complete system development (Excel/VBA/C++) of a derivatives pricing tool

Review of other technologies used in practice, including Java, COM, Python, .NET, C#, F#
ECOM003 Econometrics A
The purpose of this module is to provide students with the necessary tools for formalising a hypothesis of interest and testing it, writing a simple econometric model, estimating it and conducting inference.
Topics include:
 Review of the classical linear model
 Analysis of finite sample and asymptotic properties of ordinary least squares, instrumental variables and feasible generalised least squares, under general conditions
 Classical tests, general Hausman tests, moment’s tests
 Dependent stationary observations
 Nonlinear estimation methods, and in particular the generalised method of moments
ECOM014 Time Series Analysis
This module aims to provide a foundation in time series analysis in general and in the econometric analysis of economic time series in particular, offering theory and methods at a level consonant with an advanced training for a career economist.
Topics include:
 An introduction to time series analysis for econometrics and finance
 Vector linear time series models
 Continuous time stochastic models
 Strong dependence and long memory models
 Unit roots and cointegration
ECOM025 Financial Econometrics
This module discusses econometric methodology for dealing with problems in the area of financial economics and provides students with the econometric tools applied in the area. Applications are considered in the stock, bond and exchange rate markets.
Topics include:
 Asset returns distributions, predictability of asset returns
 Econometric tests of capital markets efficiency and asset pricing models
 Intertemporal models of timevarying risk premium
 Nonlinearities in financial data
 Value at risk
 Pricing derivatives with stochastic volatility (or GARCH) models
 Modelling nonsynchronous trading
 Numerical methods in finance
ECOM026 Financial Derivatives
The purpose of this module is to provide students with the theory and practice of pricing and hedging derivative securities. All the relevant concepts are discussed based on the discrete time binomial model and the continuous time BlackScholes model.
Topics include:
 Forward and futures contracts, swaps, and many different types of options
 Equity and index derivatives, foreign currency derivatives and commodity derivatives, as well as interest rate derivatives
 Incorporation of credit risk into the pricing and risk management of derivatives
 Extensions to the BlackScholes model
ECOM050 Investment Management
This module offers a high level introduction to concepts related to investment analysis.
Topics include:
 Valuation of real and financial securities
 The principles of investment
 Valuation of risky securities
 Portfolio analysis and bond portfolio management
 Financial market equilibrium
 The CAPM and APT models
 Capital budgeting and risk
 Market efficiency
ECOM059 Applied Risk Management for Banking
The aim of this module is to present the strategic concepts in the risk management activities of financial institutions, and in particular the processes employed in management of various risk types. You will learn how to analyse the issues, and to formulate, justify and present plausible and appropriate solutions to identified problems.
Topics include:
 Risk identification and ranking, risk appetite
 The global financial crisis of 2008
 Credit risk, credit ratings, CDS spreads, credit derivatives
 Market risk
 Liquidity risk
 Regulatory risk, regulatory capital requirements, Basel III
 The various forms of operational risk
ECOM065 Investments
This module introduces the key principles in asset pricing and investment management.
Topics include:
 Risk, return and portfolio construction
 Equity markets and pricing
 Fixed income markets and the term structure of interest rates
 Introduction to derivatives markets
 Applied security analysis
 Applied portfolio management
ECOM076 Alternative Investments
This module provides a thorough overview of recent developments in investment strategies including a description of the peculiarities of alternative asset classes. The main emphasis will be on the various complementary investment vehicles, methods and industries, namely commodities, real estate and hedge funds.
Topics include:
 Commodities, metals, energy and agriculture
 Alternative real estate financing and investment vehicles
 Analysis of hedge fund strategies
 Overview of additional alternative investments such as socially responsible funds, microfinance funds and other alternative investments
ECOM077 Valuation and Private Equity
Private equity is a relevant source of capital for companies, and a primary purpose of this module is to explore the “private equity cycle”. As valuation plays a crucial role in this cycle, the course starts with valuation techniques: from traditional methods as DCF to more recent methodologies as real options. Strong emphasis is given to practical applications: a DCF model for a "target" company will be developed inclass and a real world case of Private Equity transaction will be exposed.
Topics include:
 Private equity cycle: fundraising and structure, investing and exit
 Valuation methodologies
 Practical applications
ECOM091 Credit Ratings
This module provides an overview of credit ratings, risk, analysis and management, putting considerable emphasis on practical applications. The module gives training to students and professionals wishing to pursue a career in credit trading, financial engineering, risk management, structured credit and securitisation, at an investment bank, asset manager, rating agency and regulator; as well as in other sectors where knowledge of credit analysis is required, such as insurance companies, private equity firms, pension, mutual and hedge funds. Further, it gives a unique set of perspectives on the recent developments following the financial crisis of 2007, and the intense criticism of the rating agencies and the banking industry.
Topics include:
 Introduction to credit risk
 Credit risk analysis and management
 Credit ratings agencies, the ratings process, rating types
 Rating banks, sovereign debt and structured finance instruments
 Credit risk transfer and mitigation