Credit Risk Modeling with Delayed Information

Abstract

We introduce a notion of market times that are stochastic processes in order to represent information delay in structural credit risk models. The market times are extensions of the time change process introduced by Guo, Jarrow and Zeng in the sense that each component of the market time is not required to be a stopping time. We introduce a class of market times called idempotent market times that contain natural examples including market times driven by Poisson processes. We show that any idempotent market time is hard to be a model of the time change process. We define a filtration modulated by the market time and show that it is an extension of the continuously delayed filtration that is the filtration modulated by the time change process. We show that the conditional expectations given market filtrations have some Markov property in a binomial setting, which is useful for pricing defaultable financial instruments.

Keywords: credit risk, default risk, structural model, stopping time, random time, information delay

JEL Classification: C02, D52, D8