skip to navigation skip to content
 

Electives

Students on the MPhil in Finance programme choose three electives from a number of modules offered by the Faculty of Mathematics, the Faculty of Economics, and Cambridge Judge Business School.

The electives offered may vary from year to year. The list below should therefore be regarded as illustrative:

Advanced Financial Models

Taught by the Faculty of Mathematics (part of the Maths Part III degree).

This module is an introduction to the modelling of financial derivatives. It examines:

  • Discrete-time models. Survey of minimum-variance approaches to hedging. Complete and incomplete markets; minimal martingale measure. Characterisation of lack of arbitrage. Pricing assets in multi-period models. Optimal stopping; Snell envelope; relation to pricing American options.
  • Brownian motion and stochastic calculus. Introduction to Brownian motion; hitting times; martingales. Girsanov Theorem and change of measure. Stochastic integrals; Itô's Lemma. Ornstein-Uhlenbeck process.
  • Black-Scholes model. European call option; Black-Scholes formula. Self-financing portfolios; general partial differential equation for pricing claims. Barrier and other exotic options. Computational issues.
  • Interest-rate models. One-dimensional models: Vasicek; Cox-Ingersoll-Ross. Whole yield-curve approaches: Heath-Jarrow-Morton; Gaussian random-field models; characterisation of martingale measure; structure of covariance. Pricing interest-rate claims.

Advanced Probability

Taught by the Faculty of Mathematics.

The Advanced Probability course introduces you to advanced topics in modern probability theory. The emphasis is on tools required in the rigorous analysis of stochastic processes, such as Brownian motion, and in applications where probability theory plays an important role.

A basic familiarity with measure theory and the measure-theoretic formulation of probability theory is very helpful. These foundational topics will be reviewed at the beginning of the course, but if you're unfamiliar with them we suggest consulting the literature to strengthen your understanding.

Behavioural Economics

Taught by the Faculty of Economics.

An introduction to the behavioural approach to economics, we cover behavioural game theory, neuroeconomics, cognitive biases, decision-making heuristics, intertemporal decision making, addiction, and applications to labour economics and development. The course includes both theoretical and empirical material, but a recurring theme is the importance of experimental findings both in the laboratory and in the field.

Continuous Time Finance

This course provides you with an overview of continuous-time finance methods and their applications to corporate finance and financial economics. The course is taught primarily on the basis of journal articles, supplemented with the lecturer's own teaching notes. Throughout the course you should also learn critically to assess and evaluate papers.

Important note: This course is offered biennially. If you wish to continue onto the PhD at Cambridge Judge, this course is mandatory if it's running during your MPhil year.

Economics of Networks

Taught by the Faculty of Economics.

An exciting new research programme in economics examines the origins and the implications of networks. The lectures in this course provide a rigorous introduction to this research. To master the material, you're encouraged to work out problem sets handed out during the course.

Topics covered include:

  • Network formation: strategic and random graph models
  • Games on networks
  • Networks and markets
  • Networks and politics
  • Shocks, contagion and resilience

Further Econometrics: Time Series

The Time Series Econometrics module is intended to provide applicable, if introductory knowledge of time series analysis methods. An increasing number of empirical contexts in Finance and Management now have data in the form of time series. The statistics and modelling of time series data will be very useful in any researcher's toolkit.

Game Theory & Information Economics (2018/19)

This course is for students who wish to pursue a research career in a business school and consists of a mix of lectures and seminar-based sessions in which you read, analyse and comment on selected papers. Following the course, you'll be able to leverage your course knowledge to do original research and write papers in your chosen field of research.

Topics covered include:

  • Static games of complete information (normal form games)

    • Modelling strategic interactions
    • Iterated dominance and rationalisability
    • Nash equilibrium
    • Application: imperfect competition
    • Mixed strategies

  • Dynamic games of complete information (extensive form games)

    • Extensive form and Nash equilibrium
    • Subgame perfect equilibrium
    • Application: product differentiation
    • Repeated games and one-step deviation

  • Static games of incomplete information

    • Motivation
    • Bayesian Nash equilibrium

  • Dynamic games of incomplete information

    • Perfect Bayesian equilibrium
    • Signalling

How to Do Finance

The course introduces you to the methods, approaches, and strategies of research through a few recent and promising research topics in financial economics, providing a broad overview of the key theoretical and empirical methodological issues in each topic, as well as details related to the practical skills of organising, structuring, writing, and publishing research. Experienced faculty members also share their insights on their current research and research papers.

Operations Management

This is a seminar-style course to explore research in the area of Operations Management (OM). OM focuses on the effective planning, scheduling, and control of manufacturing and service entities. As such, it is concerned with decisions and execution of processes that enable the firm to compete profitably and deal with rapidly changing environments. Achieving operations excellence is one of the most essential strategies to improve efficiency and to gain competitive advantage. 

This course introduces students to a broad range of foundational concepts, problems, strategies, and analytical methods in the operations function of a firm. Topics include problems and issues confronting operations managers such as optimal timing and sizing of capacity expansion, inventory management, and incentives. The course material also provides exposure to conceptual, analytical and empirical research and informs the students about a suite of methodological options that ought to be considered while building their subsequent research. This course covers a mix of qualitative concepts and quantitative methods such as linear programming and dynamic programming.

Industry

Taught by the Faculty of Economics.

The Industry course introduces you to the main debates, conceptual tools and empirical findings that are central to understanding British economics history during the Industrial Revolution.

Mathematical Foundations of Operations Management (2018/19)

Mathematical modelling has played a key role in both solving operations management problems and providing managerial insights. Mathematical tools such as dynamic programming and queueing theory are used to study fundamental research questions arising in process optimisation and supply chain management. Dynamic programming provides a set of general methods for making sequential, interrelated decisions under uncertainty. Queueing theory deals with the study of waiting lines in traffic control, call centre and hospital management, and booking and service systems. Revenue management is a set of analytical tools for extracting the maximum revenue by selling the right product to the right customer at the right price at the right time. Supply chain management is a set of approaches utilised to efficiently integrate different entities in an interconnected network of suppliers, manufacturers, distributes and retailers. 

The course consists of both lectures of exploring analytical tools and seminars of discussing seminal papers in the related areas, and:

  • gets you acquainted with the most important research in Operations Management
  • provides you with tools necessary to model, formulate and analyse the problems with practical backgrounds
  • stimulates your research ideas through paper discussions
  • explains key results and identify managerial insights

Numerical Solution of Differential Equations

Taught by the Faculty of Mathematics (part of the Maths Part III degree).

The goal of this module is to present and analyse efficient numerical methods for differential equations. The exposition is based on few basic ideas from approximation theory, complex analysis, theory of differential equations and linear algebra, leading in a natural way to a wide range of numerical methods and computational strategies. The emphasis is on algorithms and their mathematical analysis, rather than on applications.

The module consists of three parts: methods for ordinary differential equations (with an emphasis on initial-value problems and a thorough treatment of stiff equations), numerical schemes for partial differential equations (both boundary and initial-boundary value problems, featuring finite differences and, time allowing, finite element methods) and numerical algebra of sparse systems (inclusive of fast Poisson solvers, sparse Gaussian elimination and iterative methods). We start from the very basics, analysing approximation of differential operators in a finite-dimensional framework, and proceed to the design of state-of-the-art numerical algorithms. Time allowing, we will also consider numerical phenomena that are of interest in fluid and gas dynamics and in nonlinear dynamical systems.

Principles of Financial Regulation

This course provides a wide-ranging examination of the major themes and topics in financial regulation. The three major recurring objectives of financial regulation - financial stability; market efficiency, integrity, and transparency; and consumer protection - anchor the course. Broad topics examined include:

  • the public interest in financial regulation
  • the traditional purposes of financial regulation and how these have evolved over time
  • the main sources of financial regulation
  • the main types of regulatory intervention
  • financial innovation, competition and regulation
  • the relationship between crises and regulation

Stochastic Calculus & Applications

Taught by the Faculty of Mathematics.

This course introduces you to Itô calculus. 

  • Brownian motion. Existence and sample path properties.
  • Stochastic calculus for continuous processes. Martingales, local martingales, semi-martingales, quadratic variation and cross-variation, Itô's isometry, definition of the stochastic integral, Kunita-Watanabe theorem, and Itô's formula.
  • Applications to Brownian motion and martingales. Levy characterization of Brownian motion, Dubins-Schwartz theorem, martingale representation, Girsanov theorem, conformal invariance of planar Brownian motion, and Dirichlet problems.
  • Stochastic differential equations. Strong and weak solutions, notions of existence and uniqueness, Yamada-Watanabe theorem, strong Markov property, and relation to second order partial differential equations.
  • Stroock-Varadhan theory. Diffusions, martingale problems, equivalence with SDEs, approximations of diffusions by Markov chains.

Prerequisites: We assume knowledge of measure theoretic probability and familiarity with discrete-time martingales and Brownian motion.

The following two modules can also be taken as electives, provided you've not already taken them as a core course:

Asset Pricing II

This course builds on Asset Pricing I. Asset Pricing examines how securities are priced. From a theoretical point of view we examine models of portfolio choice and how investors allocate their wealth across assets. From an empirical point of view, we discuss the empirical success of those models and the statistical techniques used to do so.

Topics covered include:

  • Generalised method of moments
  • Equity premium puzzle and its explanations
  • Long-term return predictability
  • Impact of trading frictions on asset prices
  • Mutual funds and hedge funds

Corporate Finance II

This course studies a number of topics in empirical corporate finance including analysing investment decisions, raising capital, takeovers, corporate governance and other topics. It is research-based, covering the major empirical research papers on these topics.

Please note that if you're planning on continuing on to a PhD at the School, you will need to choose particular electives. Find out more about our PhD pathways

Applications closed

Admissions for entry in 2017/18 have now closed.

Applications for entry in October 2018 will open in September 2017.

Scholarships

Funding available to our MPhil in Finance students includes University of Cambridge scholarships, Cambridge Judge Business School bursaries and external scholarships.

Find out more about scholarships