MA322      Half Unit
Mathematics of Finance and Valuation

This information is for the 2021/22 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. This year, apart from pre-recorded lecture videos, there will be a weekly live online session of an hour. Depending on circumstances, classes might be online.”

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 2020/21: 34

Average class size 2020/21: 17

Capped 2020/21: No

Value: Half Unit

Guidelines for interpreting course guide information

Personal development skills

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