MA322      Half Unit
Mathematics of Finance and Valuation

This information is for the 2025/26 session.

Course Convenor

Dr Arne Lokka

Availability

This course is available on the BSc in Financial Mathematics and Statistics, BSc in Mathematics and Economics, BSc in Mathematics with Data Science, BSc in Mathematics with Economics, Erasmus Reciprocal Programme of Study and Exchange Programme for Students from University of California, Berkeley. This course is freely available as an outside option to students on other programmes where regulations permit. It does not require permission. This course is available with permission to General Course students.

Requisites

Pre-requisites:

Students must have completed MA321 before taking this course.

Course content

This course provides mathematical tools of stochastic calculus and develops the Black-Scholes theory of financial markets. It covers the following topics. Continuous-time stochastic processes, filtrations, stopping times, martingales, examples. Brownian motion and its properties. Construction of the Ito integral: simple integrands, Ito's isometry. Ito processes, Ito's formula, stochastic differential equations, Girsanov's theorem. Black-Scholes model: self-financing portfolios, risk neutral measure, risk neutral valuation of European contingent claims, Black-Scholes formula, Black-Scholes PDE, the Greeks. PDE techniques for derivative pricing. Implied volatility, basic ideas of calibration.

Teaching

20 hours of lectures and 10 hours of classes in the Winter Term.

Formative assessment

Written answers to set problems will be expected on a weekly basis. 

 

Indicative reading

Lecture notes will be provided.

The following books may be useful.

T. Bjork, Arbitrage Theory in Continuous Time, Oxford Finance, 2004;

A. Etheridge, A Course in Financial Calculus, CUP, 2002;

M Baxter & A Rennie, Financial Calculus, CUP, 1996;

P. Wilmott, S. Howison & J. Dewynne, The Mathematics of Financial Derivatives, CUP, 1995;

J Hull, Options, Futures and Other Derivatives, 6th edition, Prentice-Hall, 2005.

D. Lamberton & B. Lapeyre, Introduction to stochastic calculus applied to finance, 2nd edition, Chapman & Hall, 2008.

S. E. Shreve, Stochastic Calculus for Finance. Volume I: The Binomial Asset Pricing Model. Springer, New York, 2004.

S. E. Shreve, Stochastic Calculus for Finance. Volume II: Continuous-Time Models. Springer, New York, 2004.

Assessment

Exam (100%), duration: 120 Minutes in the Spring exam period


Key facts

Department: Mathematics

Course Study Period: Winter Term

Unit value: Half unit

FHEQ Level: Level 6

CEFR Level: Null

Total students 2024/25: 17

Average class size 2024/25: 9

Capped 2024/25: No
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Personal development skills

  • Self-management
  • Problem solving
  • Communication
  • Application of numeracy skills
  • Specialist skills