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Module Title Mathematical Finance
SchoolMathematics
Department Mathematics
Module Code 06 20443
Module Lead JJ Ruckmann
Level Masters Level
Credits 20
Semester Full Term
Pre-requisites Discrete Mathematics and Statistics - (06 22513) Analytical Techniques - (06 22488)
Co-requisites
Restrictions Optional for MSci programmes in Mathematics, MSci programmes with Major in Mathematics, MSci programmes with Joint (60 credits) in Mathematics
Contact Hours Lecture-46 hours
Tutorial-10 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 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 90% based on a 3 hour written examination in the Summer Term; 10% based on work during term-time.
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;