Modeling and pricing credit derivatives

Credit derivatives often show an appealing risk-return profile for investors. They allow for an enhancement of portfolio returns, but also offer high potential for risk diversification, due to the correlation structure of their returns to those of traditional asset classes. Beside corporate bonds, we therefore review popular credit derivatives and present a mathematical definition of their payoff structures. To actually price credit derivatives, we discuss the most important models and theoretical developments of the past years. Structural-default models assume that the dynamics of the firm's asset value over time can be described as a stochastic process and that the defaultable security can be regarded as a contingent claim on this value. Intensity-based models do not consider the relation between default and asset value in an explicit way. They rather specify the default process exogenously and model default as the stopping time of some given hazard-rate process. While reduced-form models have attractive properties, their main drawback is the missing link between economic fundamentals and corporate defaults. Hybrid models try to overcome this shortfall and combine the advantages of structural and intensity-based models. Correlated changes in revenues and costs of different companies usually influence the default probability of these firms. We will thus present different approaches for the modeling of joint defaults and give some algorithms to show how these approaches can be implemented for the pricing of portfolio-credit derivatives.