# Programme Outline, Dissertation & Modules

**Programme Outline**

Students must take a total of eight taught modules, as specified in the list below. There is also an unassessed pre-sessional 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 in-term 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 Pre-sessional 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 Black-Scholes 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 object-oriented 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 object-oriented programming: Objects and classes
- Examples from finance including bond pricing, histogramming historical price data, option pricing and risk management within the Black-Scholes 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 discrete-time binomial model and the continuous-time Black-Scholes model.

Topics include:

- Review of key concepts in probability theory
- Introduction to financial markets
- Pricing derivatives by no-arbitrage arguments
- Discrete-time option pricing models
- Introduction to continuous-time stochastic processes and the Black-Scholes model

#### MTH772P Stochastic Calculus and Black-Scholes 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 no-arbitrage principle can be used to derive the famous Black-Scholes formula for European call options. We further develop the concepts of risk-neutrality and market completeness. Finally, we apply the methods of stochastic calculus to price different kinds of financial derivative, including exotic and American-style options.

Topics include:

- Overview of continuous-time 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 Black-Scholes formula for European call options, and the BS partial differential equation
- Fundamental theorems of asset pricing
- Constructing risk-neutral 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 object-oriented 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 yield-to-maturity, discount factor curve bootstrapping, stochastic interest rate models)
- Numerical methods (interpolation, numerical quadrature, non-linear solvers, binomial trees (Cox-Ross-Rubinstein), Monte Carlo methods, finite-difference 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 word-processed pages (10,000 words), securely bound, covering a specific research-level 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
- Jump-diffusion models for equity prices
- Passport options
- Pricing and risk-management 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 dynamically-linked 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 co-integration

#### 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
- Inter-temporal models of time-varying risk premium
- Non-linearities in financial data
- Value at risk
- Pricing derivatives with stochastic volatility (or GARCH) models
- Modelling non-synchronous 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 Black-Scholes 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 Black-Scholes 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 in-class and a real world case of Private Equity transaction will be exposed.

Topics include:

- Private equity cycle: fund-raising 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