Mathematical Finance

This is a year two module.  It is taught intensively by Birmingham professors over eight weeks.  There is continuous assessment and a final examination.

Financial derivatives are examined using a continuous-time approach, examining the relevant partial differential equations and boundary conditions in a number of different problems. The solution method is examined, using a mix of analytical and computational methods. A range of discrete time financial models is analysed. This includes mainly (but not exclusively) the return of assets and their volatility, two-asset and multi-asset portfolio optimisation and various investment models such as options, futures and bonds.

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 how interest calculations, asset return and investment types such as bonds, future and options, and of how investment portfolios of risky assets should be composed in order to obtain a desired return with minimum risk