Pre-requisite modules
Co-requisite modules
- None
Prohibited combinations
- None
Occurrence | Teaching period |
---|---|
A1 | Semester 1 2024-25 |
A2 | Semester 1 2024-25 to Semester 2 2024-25 |
B1 | Semester 2 2024-25 |
B2 | Semester 2 2024-25 |
The module introduces the probabilistic concepts and techniques necessary for modelling the dynamics of interest rates. The mathematical theory of interest rates is complex, since on the one hand it has to cover simultaneous random behaviour of a family of bonds indexed by maturity, and on the other hand be consistent with no-arbitrage restrictions. Additionally, to be realistic models have to be complex enough to enable the calibration of their parameters to real data. The complexity stems from the fact that in general interest rates depend on running time and maturity time, so are stochastic processes of two time variables, each with a very specific role. Discrete models will be constructed based on tree structures. For some special models a continuous time limit results in a stochastic differential equation of Ito type. In full generality the theory of partial stochastic differential equations is needed to investigate sophisticated models (this issue is only briefly outlined in the module). However, there is no such thing as the best or universally accepted model. Hence this module shows a variety of approaches and much time is devoted to the study of their relationships. One crucial issue is concerned with fitting the model to the data, called calibration. Pricing interest rate derivative securities is of great importance, since they represent a vast majority of the derivatives traded.
By the end of this module students should
Task | % of module mark |
---|---|
Coursework - extensions not feasible/practicable | 100 |
Oral presentation/seminar/exam | 0 |
None
Task | % of module mark |
---|---|
Coursework - extensions not feasible/practicable | 100 |
Oral presentation/seminar/exam | 0 |
Information currently unavailable
1. M. Capinski and T. Zastawniak, Mathematics for Finance, Chapters 10, 11. Springer-Verlag, London 2003.
2. R. Jarrow, Modelling Fixed Income Securities and Interest Rate Options, McGraw-Hill, New York 1996.
3. T. Bjork, Arbitrage Theory in Continuous Time, Oxford University Press, Oxford 1998.