Credit derivatives pricing with default density term structure modelled by L\'evy random fields

TL;DR

This paper introduces a novel approach to credit derivatives pricing by modeling the default density term structure with Le9vy random fields, accounting for contagious jump risks and default recovery payments.

Contribution

It develops a Le9vy random field-based model for default intensity and density, providing a new framework for pricing defaultable bonds with jump risk considerations.

Findings

Contagious jump risks significantly affect bond prices.

The pricing kernel is characterized as a solution to a parabolic integro-differential equation.

Numerical examples demonstrate the model's impact on defaultable bond valuation.

Abstract

We model the term structure of the forward default intensity and the default density by using L\'evy random fields, which allow us to consider the credit derivatives with an after-default recovery payment. As applications, we study the pricing of a defaultable bond and represent the pricing kernel as the unique solution of a parabolic integro-differential equation. Finally, we illustrate by numerical examples the impact of the contagious jump risks on the defaultable bond price in our model.