Dynamic credit models

Abstract

We present a dynamic framework to model the default events of individual obligors and the correlation between these default events. For the first purpose, we present the concepts of the dynamic jump-to-default model. For the second purpose, we concentrate on factor models which describe default events within a basket of obligors. In contrast to previous studies of factor credit models, we do not restrict ourselves to tractable, but not necessarily financially motivated, affine dynamics of the common factor and individual default intensities. Instead, we model the defaults using the logit survival function which depends on an appropriately chosen common factor. In the static version of the model, the distribution of the common factor is discrete, while in the dynamic version of the model the evolution of the common factor is driven by a jump-diffusion stochastic process. To solve the calibration and pricing problem, we develop robust partial integro-differential equation (PIDE) based numerical solution methods for the forward and backward Kolmogoroff equations. We also show how to augment the pricing problem with the loss intensity rate, and apply it to price structured credit products within the dynamic model. Finally, we provide an example of calibrating both the static and dynamic models to iTraxx credit index data.