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

Mode of delivery

face to face



Recommended or required reading and other learning resources/tools

Hull, J. (2005). Options, Futures, and other Derivatives, 6th edition. Financial Times. Bluhm, C., Overbeck, L. and Wagner, C. (2003). An Introduction to Credit Risk Modelling. Chapman&Hall/CRC.

Planned learning activities and teaching methods

The classes will contain lectures as well as implementation exercises, optionally via spreadsheets or programming. Students are asked to bring their computers with software ready for use (spreadsheets, ideally GNU/R or some other programming environment). Three take-home assignments will further strengthen implementation skills.

Assessment methods and criteria

The grade will depend on the final exam (70%) and three take-home assignments plus class participation (10% each). The first assignment will be handed out in Class 1 and be due for Class 2; the second assignment will be from Class 3 to Class 4; the third assignment is provided in Class 5 and discussed in Class 6. The final exam will last 90 minutes and focus on understanding and applying the concepts rather than straight reproduction.

Prerequisites and co-requisites

Courses in quantitative methods


Degree programme

Quantitative Asset and Risk Management (Master)



ECTS Credits


Language of instruction




Academic year



1 WS



Learning outcome

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.

Course code