Aims

The aim of the module is to present classical mathematical approaches to portfolio selection and asset pricing in discrete time.

Learning objectives

At the end of the module you should be be familiar with:

• basic discrete time market models
• the rationale behind portfolio selection in discrete time
• main ideas behind pricing of forward contracts and options in discrete time

Syllabus

• Introduction: What is Mathematical Finance
• Discrete time market models
• No-Arbitrage Principle
• Portfolio Selection
• CAPM
• Forward Contracts
• European and American Options

Recommended texts

Core Texts for Finance I and II:

• M. Capinski and T. Zastawniak, Mathematics for Finance. An Introduction to Financial Engineerin, Springer (G 2.01 CAP)
• M.J. Seele, Stochastic Calculus and Financial Applications, Springer (S 9.3 STE)
• M. Baxter and A Rennie, Financial Calculus: An introduction to derivative pricing, Cambridge University Press (G 2.01 BAX) only for Finance II

Supplementary/Additional Texts for Finance I and II:

• J. Cvitanic and F. Zapatero, Introduction to the Economics and Mathematics of Financial Markets (G 2.01 CUI)
• P. Wilmott, Paul Wilmott introduces Quantitative Finance, Wiley (G 2.01 WIL)
• P. Wilmott, Paul Wilmott on Quantitative Finance (2 vols), Wiley (G 2.01 WIL)
• S. Benninga, Financial Modeling (G 2.01 BEN)
• C. H. Huang and R. H. Litzenberger., Foundations for Financial Economics (G 2.6 HUA)
• S. R. Pliska, Introduction to Mathematical Finance, Blackwell (G 0.182 PLI)
• J. E. Ingersoll, Theory of Financial Decision Making, Rowman and Allanheld (G 2.01 ING) only for Finance I

Teaching

• Autumn Term
• 2 lectures per week 
• 1 problems class per week.

Assessment

Students taking Mathematical Finance I and II: three hour closed examination towards the end of the Summer Term (90%).

Students taking only Mathematical Finance I take part of the paper in a one and a half hour examination (90%).

Coursework 10%. Note that coursework submitted after the advertised deadlines will be given a mark of zero.

Special note for students who wish to seek exemptions from some Institute of Actuaries subject examinations:

We are currently engaged in discussions with the Institute of Actuaries concerning exemptions from Subject CT8.

Those students seeking exemptions, because they are wishing to enter the Actuarial Profession, should be aware that they will be required to:

• take Stochastic Calculus (0590318) and both terms of Mathematical Finance;
• in the third terms attend additional seminars devoted to actuarial topics.

They are likely to be asked to sit an additional (shorter) examination paper covering material from the extra seminars.

Elective information

This module is not available as an elective.

Prerequisites

• Linear Algebra
• Statistical Theory 1
• Probability Theory 1