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 Black-Scholes 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
20443-10 : Raw Module Mark : Coursework (100%)
Assessment Methods & Exceptions
3 hour Written Unseen Examination (80%); In-course Assessment (20%)
Other
None
Reading List
'The Mathematics of Financial Derivatives: A Student Introduction¿ by Paul Wilmott, Sam Howison and Jeff Dewynne. 1995. ISBN 0521497892. Published by Cambridge University Press;
`Options, futures and other derivatives¿ by John C. Hull (6th edition) 2006. ISBN 0131499068. Published by Prentice Hall;
