Module Title  Mathematical Finance 
School  Mathematics 
Department  Mathematics 
Module Code  06 20443 
Module Lead  JJ Ruckmann 
Level  Masters Level 
Credits  20 
Semester  Full Term 
Prerequisites 
Discrete Mathematics and Statistics  (06 22513)
Analytical Techniques  (06 22488)

Corequisites 

Restrictions  Optional for MSci programmes in Mathematics, MSci programmes with Major in Mathematics, MSci programmes with Joint (60 credits) in Mathematics 
Contact Hours 
Lecture46 hours
Tutorial10 hours
Total: 56 hours

Exclusions  
Description  Financial derivatives will be examined, examining the relevant differential equations and boundary conditions in a number of different problems. The solution method will also be examined, using a mix of analytical and computational techniques. Topics:
1. Introduction to financial mathematics
2. Introduction to financial derivatives
3. Derivation of the BlackScholes equation
4. European options
5. American options
6. Analytical methods for the solution of option problems
7. Computational methods for the solution of option problems
8. Advanced topics. 
Learning Outcomes  By the end of the module the student should be able to: Write down the governing partial differential equations and boundary conditions for a range of financial derivative problems
 Solve the relevant partial differential equations arising from the study of some financial derivative problems using analytical and computational methods
 Demonstrate an understanding of how mathematics and in particular discrete mathematics is used in the financial sector of the economy
 Demonstrate an understanding of interest calculations, asset return and investment types such as bonds, futures and options, and of how investment portfolios of risky assets should be composed in order to obtain a desired return with minimum risk
 Explore these topics beyond the taught syllabus

Assessment 
2044310 : Raw Module Mark : Coursework (100%)

Assessment Methods & Exceptions  90% based on a 3 hour written examination in the Summer Term; 10% based on work during termtime. 
Other  None 
Reading List 
`Options, futures and other derivatives¿ by John C. Hull (6th edition) 2006. ISBN 0131499068. Published by Prentice Hall;
'The Mathematics of Financial Derivatives: A Student Introduction¿ by Paul Wilmott, Sam Howison and Jeff Dewynne. 1995. ISBN 0521497892. Published by Cambridge University Press;
