Course Catalogue

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The aim of this course is to provide an overview of the uses of mathematics and statistics in finance. The course will provide details of some probabilistic and statistical methods used in finance. Applications of mathematical, optimisation and probabilistic methods from other courses will be described. An introduction to the ideas of derivative pricing, portfolio management will be provided.

17 x 1 hr lectures and 6 x 1 hr tutorials in a semester

The normal requirement is that students should have been admitted to an Honours- or Master's-level programme in Mathematics and/or Statistics.

5E: Mathematical Finance

End-of-Course Examination 90%

Coursework 10%

Reassessments are normally available for all courses, except those which contribute to the Honours classification. Where, exceptionally, reassessment on Honours courses is required to satisfy professional/accreditation requirements, only the overall course grade achieved at the first attempt will contribute to the Honours classification. For non-Honours courses, students are offered reassessment in all or any of the components of assessment if the satisfactory (threshold) grade for the overall course is not achieved at the first attempt. This is normally grade D3 for undergraduate students and grade C3 for postgraduate students. Exceptionally it may not be possible to offer reassessment of some coursework items, in which case the mark achieved at the first attempt will be counted towards the final course grade. Any such exceptions for this course are described below. 

To provide an overview of the uses of mathematics and statistics in finance;

To provide details of some probabilistic and statistical methods used in finance;

To describe applications of mathematical, optimisation and probabilistic methods from other courses;

To provide an introduction to the ideas of derivative pricing, portfolio management.

By the end of this course students will be able to:

■ to explain the idea of time value of money, interest rates, and the arithmetic of compounding and discounting; and to implement these concepts by performing concrete computations;

■ to describe basic financial products (bonds, stocks) and explain and apply the idea and terminology of futures contracts (long, short positions, hedging, arbitrage);

■ to explain basic concepts and principles of mathematical finance in the context of one-period models (arbitrage, risk-neutral measures), and to apply these concepts in finite market models and perform example computations;

■ to describe the basic terminology for options (call, put, American, European) as well as be able to create graphs and explain their payouts;

■ to explain how options can be implemented in one-period market models, how inequalities for their prices can be derived and the concept of market completeness; to apply these concepts;

■ to explain and apply the basic concepts of mathematical finance in the context of multiperiod models (price- and value processes, arbitrage, martingale measures), to describe their manifestation in the particular case of the CRR (or binomial) model, and to carry out calculations for pricing options in this model;

■ to derive the Black-Scholes model by considering limits of discrete time models, and to use it to price contingent claims

■ to describe the properties of the Black-Scholes model using geometric Brownian motions and Ito's formula

■ to explain and apply different approaches to measure and manage risk (e.g. the Greeks, Value-at-Risk, the mean-variance approach

Students must submit at least 75% by weight of the components (including examinations) of the course's summative assessment.