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Electives on the MPhil in Finance

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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. All courses are taught at the School unless specified otherwise.

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

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.

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.

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.

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.

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.

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

In a large number of empirical contexts in finance and management, data are temporarily ordered in the form of time series. The Time Series Econometrics module introduces you to concepts and methods that are appropriate for empirical research in such settings, covering methods for exploratory time series analysis, estimation of dynamic causal effects and forecasting.

Taught by the Faculty of Economics.

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

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.

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.

This course offers training in the basic techniques of financial accounting and then introduces you to select applied settings that use financial reporting information for valuation and investment decisions.

The course first focuses on building a foundation of knowledge for understanding accounting measurement and reporting. Accounting is in essence a model for recording and presenting economic information, and the starting point is to grasp how this model works and understanding its strengths and limitations.

The second part of the course exposes you to select applied topics such as public equities, private equity, and venture capital for valuation and investment decisions. Industry experts feature as guest lecturers in the second part of the course.

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

This course builds upon Asset Pricing I. Asset Pricing II examines how assets are priced in practice and how pricing models are implemented via basic trading strategies.

The course is delivered using lecture slides, Jupyter notebooks, and a free online platform for building and backtesting algorithmic strategies (Quantopian). Some knowledge of Python would be helpful (although not a prerequisite).

Topics covered include:

  • Asset pricing: foundations and quantitative implementation
  • Valuing risk
  • Estimation techniques and model selection
  • Hypothesis testing
  • Small sample inference
  • Modelling, estimating and forecasting volatility
  • Introduction to machine learning

This course studies a number of topics in empirical corporate finance, including analysing investment decisions, raising capital, takeovers, private equity, venture capital, corporate governance, fraud 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.

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