MSc Mathematical Finance

This module aims to develop and support the skills required for practical applications of theoretical concepts developed elsewhere in the course.  

Objectives: 

• To develop an understanding of the concepts and “way of thinking” of (object-oriented) programming in general, and practical programming ability in a selection of languages in particular. 

• To provide a framework in which theoretical concepts and methodology developed in the core learning can be tested and applied to “real world” problems, thus reinforcing both the theoretical concepts as well as practical programming skills. 

• To develop a set of transferrable skills required/desired by employers in the Quantitative Finance industry, enhancing students’ competitive “edge” in the job market and widening their choice of attainable career destinations. 

Upon completing this module, you will be able to 

• Define and explain, both intuitively and formally, the concept of “object-oriented programming” and “application design”. 

• Understand and explain the common and distinct features, including syntax, of a variety of programming languages. 

• Build applications “from scratch” to accomplish tasks and/or solve “real world” problems in Quantitative Finance. 

• Identify, acquire and use public code libraries to incorporate in their own applications to achieve tasks as in 3 above. 

This module will provide a thorough introduction into discrete-time martingale theory, Brownian motion, and stochastic calculus, illustrated by examples from Mathematical Finance. 

Upon completing this module, you will be able to 

• explain and apply the concept of measure-theoretic conditional expectations 

• demonstrate an understanding of discrete time martingale theory and apply the theory to option pricing 

• understand the basic properties of Brownian motions 

• explain the main steps in the construction of the stochastic integral 

• be proficient in applying Ito’s formula and Girsanov’s theorem in problems arising in Mathematical Finance 

• solve standard SDEs appearing in Mathematical Finance 

This module will introduce you to the main approaches to statistical inference and financial time series. 

Upon completing this module, you will be able to analyse, explain and apply the statistical techniques to finance. 

The main aim of this module is to introduce you to modern theories of Asset Pricing and Portfolio Theory in both static and dynamic settings. The key is the modelling and measurement of uncertainty (risk), how investors make decisions in the presence of such uncertainty, and how such behaviours drive both time series and cross-section of asset prices and returns in equilibrium.  

The main objectives are to develop a solid understanding of the theoretical framework, the ability to interpret and critically evaluate existing and new theoretical and empirical literature, and the skills and methodologies to apply the theory to practical problems. 

As the “foundation stone” of one of the four pillars of the MSFM architecture, this module is closely integrated with the other Term 1 core modules.  

Upon completing this module, you will be able to: 

• Define and explain, intuitively and formally, the fundamental trade-off between risk and return, and how this can be modelled and quantified. 

• Understand and explain different models that describe how individuals make decisions in the presence of uncertainty, and how such behaviours affect asset prices and returns in equilibrium. 

• Devise and implement empirical methodology to a) estimate the parameters of, and b) assess the validity of, a variety of different asset pricing models. 

This module will introduce you to the main tools and approaches to estimation and inference of financial and economic models. 

Upon completing this module, you should be able to estimate and make inference of main econometrics models, both linear and non-linear; and should be able to handle and apply statistical and econometric tools to high-frequency data. 

This module will help you to gain thorough understanding of how stochastic calculus is used in continuous time finance. You will also develop an in-depth understanding of models used for various asset classes. 

Upon completing this module, you will be able to: 

• price European options via EMM and PDE techniques 

• carry out computations for various stochastic volatility models 

• explain the different approaches to model interest rates 

• describe and price main credit derivatives 

• discuss the properties of FX markets and carry out relevant calculations. 

The 10,000 word dissertation allows you to synthesise, apply and extend the knowledge you have gained in the taught component of the programme, and to demonstrate mastery of some elements of financial mathematics. 

You will also demonstrate an in-depth comprehension of an area of financial mathematics. 

The focus of the dissertation may be to: 

• Implement and provide a critical analysis of a set of quantitative models used in finance 

• Use market data in performing statistical tests of a set of financial hypotheses 

• Synthesise an area of theoretical research in financial mathematics, extending knowledge where possible and demonstrating mastery of the subject by expanding on the arguments given in the literature. 

You will be supervised and supported by one of our academic staff.