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MA322 Half Unit

Mathematics of Finance and Valuation

**This information is for the 2022/23 session.**

**Teacher responsible**

Dr Albina Danilova COL.4.09

**Availability**

This course is available on the BSc in Financial Mathematics and Statistics, BSc in Mathematics and Economics and BSc in Mathematics with Economics. 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.

**Pre-requisites**

Students must have completed Measure Theoretic Probability (MA321).

**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**

This course is delivered through a combination of classes and lectures totalling a minimum of 30 hours across Lent Term.

**Formative coursework**

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: 2 hours) in the summer exam period.

** Key facts **

Department: Mathematics

Total students 2021/22: 24

Average class size 2021/22: 12

Capped 2021/22: No

Value: Half Unit

**Course 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