Dr Arne Lokka

This course is compulsory on the MSc in Financial Mathematics. This course is available on the MSc in Risk and Stochastics, MSc in Statistics (Financial Statistics) and MSc in Statistics (Financial Statistics) (Research). This course is available with permission as an outside option to students on other programmes where regulations permit.

Students must have completed The Mathematics of the Black and Scholes Theory (MA415).

This course is concerned with the mathematical foundations of interest rate and credit risk theory. The course starts with a development of the multi-dimensional Black & Scholes theory with stochastic market data. This is then used to show how discount bond dynamics modelling can be approached by (a) the modelling of the short-rate process and the market price of risk, which underlies the family of short-rate models, or (b) the modelling of the market price of risk and the discount bond volatility structure, which gives rise to the Heath-Jarrow-Morton (HJM) framework. The course then expands on the theory of interest rate market models and credit risk.

20 hours of lectures and 10 hours of seminars in the LT.

T R Bielecki and M Rutkowski, Credit Risk Modeling, Valuation and Hedging, Springer; J James and N Webber, Interest Rate Modelling, Wiley; A J McNeil, R Frey, and P Embrechts, Quantitative Risk Management: Concepts, Techniques, and Tools, Princeton University Press; M Musiela and M Rutkowski, Martingale Methods in Financial Engineering, Springer; R Rebonato, Modern Pricing of Interest-rate Derivatives: The LIBOR Market Model and Beyond, Princeton.

Exam (100%, duration: 2 hours) in the main exam period.