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: NoCourse selection videos
Some departments have produced short videos to introduce their courses. Please refer to the course selection videos index page for further information.
Personal development skills
- Self-management
- Problem solving
- Communication
- Application of numeracy skills
- Specialist skills