Introduction to the mathematical theory of popular term structure models and to the concepts of credit risk modelling, risk aggregation and credit risk management. Special emphasis is given to practical aspects.

(I) Models in discrete time - Basic theory of interest (present value, internal rate of return, yield, duration, convexity, immunization) - Forward rates and term structure explanations, expectation dynamics - Binomial lattices and binomial trees for pricing interest rate derivatives, leveling - Bernoulli and Poisson mixture models for credit risks - CreditRisk+ and its extensions, numerically stable algorithm for its implementation (II) Models in continuous time - Brief review of Brownian motion, stochastic integrals and stochastic differential equations - Models for the short rate of interest (Vasicek model, Cox-Ingersoll-Ross model, affine models) - Forward rate models (Heath-Jarrow-Morton model) - Firm value (structural) models for credit risks (Merton, KMV) - Intensity based models for credit risks (III) Practical aspects - Securitization of loans and mortgages - Credit derivatives - Regulatory capital requirements for banks

Active participation in the exercises, oral examination

No lecture notes are available.