MSc Mathematical Finance

Course Details

Seven compulsory modules cover the four key pillars of the core skill set needed for a career in the finance industry: Financial Statistics, Financial Mathematics, Asset Pricing and Risk, and Simulation and Machine Learning for Finance. Alongside this, you'll learn programming for Quantitative Finance, focusing on C++, Python, and R.

Our optional modules enable you to personalise the course to your own interests, allowing you to focus on your future career path in finance. Please note that availability and delivery modes may vary.

Modules are taught by staff from WBS, Warwick's Department of Statistics, and the Mathematics Institute through a combination of lectures, classes, and computer lab sessions. A one-week induction module will ensure you have the mathematical and statistical prerequisites for the course. Assessment is a mix of exams and coursework with your dissertation bringing all your learning together at the end.

Lectures & classes
Lectures introduce key theories, concepts, and economic models. You will solve financial problems and numerical exercises, analyse case studies, and make presentations of research published in academic journals.

Lab work
Lab work will give you hands-on experience of using software to perform finance-related calculations, conduct realistic simulations and write code. 

Learn from the practitioners
Guest lectures by practitioners from the quantitative finance industry will give an applied context to your course, showcasing how the course prepares you for a variety of graduate destinations, and giving valuable networking opportunities.

External companies also provide a selection of dissertation projects for our students, giving the opportunity for you to apply your knowledge in a real corporate setting.

Learning facilities
You will have access to our outstanding learning facilities, including a Postgraduate-only Learning Space and IT suite, as well as all other University facilities. Studying on a Finance-based MSc also means that you gain access to our Bloomberg terminals, Eikon terminals, and financial data via the Wharton Research Data Services.

Your dissertation
A 10,000 word dissertation gives you the opportunity to test and apply techniques and theories you have been learning and to complete an original piece of research. You will be supervised and supported by one of our academic staff.

 

 

 

Compulsory Modules

Programming for Quantitative 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 MSFM core 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. 

Stochastic Calculus for Finance

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 

Financial Statistics

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. 

Simulation & Machine Learning for Finance

This module will provide both a theoretical and a practical understanding of numerical methods in finance, in particular those related to simulations of stochastic processes and machine learning. 

Asset Pricing & Risk

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. 

Financial Econometrics

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. 

Applications of Stochastic Calculus in Finance

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. 

Dissertation

The 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. 

Example Optional Modules

Behavioural Finance

Psychologists working in the area of behavioural decision-making have evidenced the inadequacies of neoclassical economics. In this module you will study financial markets using models that are less narrow than those based on von Neumann-Morgenstern expected utility theory and arbitrage assumptions.

Statistical Learning & Big Data

On this module you will cover:

  • Statistical Learning
    • An introduction to statistical learning theory: from over-fitting to apparently complex methods which can work well. For example, VC dimension and shattering sets, PAC bounds.
    • Loss functions. Risk (in the learning theory sense); posterior expected risk. Generalisation error.
    • Supervised, unsupervised and semi-supervised learning.
    • The use of distinct training, test and validation sets particularly in the context of prediction problems.
    • The bootstrap revisited. Bags of little bootstraps. Bootstrap aggregation. Boosting.
    • ML method will be used to illustrate these ideas.
  • Big data and big model related issues and (partial) solutions
    • "Curse of dimensionality". Multiple testing: voodoo correlations; false-discovery rate and family-wise error rate; corrections: Bonferroni, Benjamini-Hochberg.
    • Sparsity and regularisation. Variable selection; regression. Spike and slab priors. Ridge regression. The Lasso. The Dantzig selector.
    • Concentration of measure, related inferential issues.
    • MCMC in high dimensions, preconditioned Crank Nicolson; MALA; HMC. Preconditioning. Rates of convergence.

 

Brownian Motion

Brownian motion is a fundamental tool for modelling processes which evolve randomly in time and underpins almost all stochastic models for asset prices in finance. In this module you will learn how to construct Brownian motion and study its path properties, how to use stochastic calculus for manipulations, and about differential equations. This will enable you to understand and develop state-of-the-art stochastic models in finance. 

Advanced Trading Strategies

This module aims to provide you with an introduction to three advanced topics in Mathematical Finance. You will be able to compute and explain key variables in the relevant models, apply appropriate mathematical techniques, and analyse and compare different modelling approaches.

Three topics will be covered each year, motivated by current questions relevant to the financial industry. Example topics are algorithmic trading, introduction to market microstructures, limit order books.

Partial Differential Equations in Finance

Gain a theoretical and practical understanding of partial differential equations, including numerical methods; link this understanding with problems from finance; gain an introduction to optimal control and Markov chain Monte Carlo (MCMC) methods.

Advanced Risk Management

Module info TBC

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