Fixed Income and Credit Derivatives
Introduction to Fixed Income: Interest Rates, Fixed-Income Instruments, Basic ideas of pricing fixed-income products. Term Structure Models: Nelson-Siegel-Svensson, Cubic Splines, Parameter Forecasting. Interest Rate Derivatives: Callable Bonds, Interest-Rate Caps and Floors, Swaptions. Short-Rate Modelling: Introduction to models like Vasicek, Cox-Ingersoll-Ross, Ho-Lee. Interest-Rate Trees. Credit derivatives: Institutional background, common instruments and indices, market conventions; Credit Ratings; Fundamental concepts of credit-risk modelling. Rating-based models: Transition probabilities, migration matrices, Markov chains and generator matrices; Simulation; Pricing. Structural models: Merton model, risk structure of credit spreads, seniority structure; Simulation. Black-Cox model, KMV model; Capital structure. Intensity models: Discrete-time martingale models and implied pricing probabilities; Building blocks for pricing. Poisson processes, constant and deterministic default intensity; Cox processes, stochastic default intensity and affine models. Factor models: Concepts, conditional default probabilities, loss distributions, risk parameters, scenario stress-testing. CDO pricing: Homogeneous large portfolios and Gaussian copulas, tranche pricing; Compound, base and implied correlations; Bootstrapping
Quantitative Asset and Risk Management (Master)
Language of instruction
Successful students will have gained a basic understanding concerning the pricing of derivative instruments under the no-arbitrage principle. They will be able to outline explicit methods for the pricing of fixed-income and credit derivatives and to apply those.