Dr Jon Danielsson and Dr Rohit Rahi

This course is compulsory on the BSc in Financial Mathematics and Statistics. This course is available on the BSc in Accounting and Finance, BSc in Business Mathematics and Statistics, BSc in Econometrics and Mathematical Economics, BSc in Economics, BSc in Mathematics and Economics, BSc in Statistics with Finance and Diploma in Accounting and Finance. This course is available as an outside option to students on other programmes where regulations permit. This course is available with permission to General Course students.

Students must have completed Principles of Finance (FM212), Mathematical Methods (MA100) and Elementary Statistical Theory (ST102).

Introduction to Econometrics, Principles of Econometrics or other statistics courses where at least linear regression models are covered are recommended but not required. Students who have not taken Principles of Finance, but have an excellent quantitative background, may be allowed to take this course at the discretion of the course leader.

This course is intended for third-year undergraduates and builds upon FM212 Principles of Finance. The main topics covered are financial risk analysis and financial risk management (first part of the course) and derivatives pricing (second part). As such, this course is complementary to FM300 Corporate Finance, Investments and Financial Markets, with minimal overlap.

The first part of the course provides students with a thorough understanding of market risk from both a practical and technical point of view. We discuss the empirical properties of market prices (fat tails, volatility clusters, etc.), forecasting of prices, concepts of financial risk (volatility, Value-at-Risk, etc.), volatility models (ARCH, GARCH, etc.), and we analyse how interactions and feedback between market players can generate endogenous risk and liquidity crises. Finally, we discuss credit markets and liquidity, with applications to the current situation in financial markets. This part of the course presents methods and models used by banks and other financial institutions in the management of risk and allocation of risk capital, as well as models of financial crises. Students apply the models to real financial data using Matlab, a computer software popular in both industry and academia. No prior knowledge of programming is assumed: students will learn-by-doing in class. Students will at times use data and software for classwork assignments.

The second part of the course focuses on derivatives, with a particular emphasis on equity derivatives (standard call and put options, exotic options), futures and forward contracts, and interest rate derivatives (swaps, caps and floors, swaptions). We systematically address three basic questions: how do these products work, i.e. what are their payoffs? How can they be used, for hedging purposes or as part of trading strategies? And above all: how are they priced? The course emphasizes a small number of powerful ideas: absence of arbitrage, replication, and risk-neutral pricing. These are typically introduced in the context of discrete-time models, but the course also covers some well-known continuous-time models, starting with a comprehensive treatment of the Black-Scholes model. The level of mathematics is appropriate for third-year students with a solid quantitative background. Continuous-time stochastic processes and stochastic calculus will be introduced as we go.

20 hours of lectures and 10 hours of classes in the MT. 22 hours of lectures and 9 hours of classes in the LT.

Students will be expected to produce written work for classes and to make positive contributions to class discussion.

J Danielsson, Financial Risk Forecasting: The Theory and Practice of Forecasting Market Risk will be the required textbook for the first half of the course. For the second half of the course, there is no required textbook, but the following is an excellent reference: J Hull, Options, Futures, and Other Derivatives.

Exam (87.5%, duration: 3 hours) in the main exam period.
Project (10%) and coursework (2.5%) in the MT.