Dr Christoph Czichowsky

This course is compulsory on the MSc in Financial Mathematics. This course is available on the MSc in Quantitative Methods for Risk Management, 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 Stochastic Processes (ST409).

This course studies 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.

This course is delivered through a combination of seminars and lectures totalling a minimum of 30 hours across Winter Term.

The main formative assessment will be in the form of weekly exercise sets, which will be discussed in the seminars. Some of the topics of these will be similar to what is expected in the summative assessment (exam).

T R Bielecki and M Rutkowski, Credit Risk Modeling, Valuation and Hedging, Springer; 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 spring exam period.