Pricing Vulnerable Claims in a Lévy Driven Model

Abstract

We obtain an explicit expression for the price of a vulnerable claim written on a stock whose predefault dynamics follows a Levy-driven SDE. The stock jumps to zero at default with a hazard rate intensity given by a negative power of the stock price.

We recover the characteristic function of the terminal log price as the solution of a complex valued infinite dimensional system of first order ordinary differential equations.

We provide an explicit eigenfunction expansion representation of the characteristic function in a suitably chosen Banach space, and use it to price defaultable bonds and stock options. We present numerical results to demonstrate the accuracy and efficiency of the method.

Keywords: default, infinite dimensional analysis, vulnerable claims, Lévy process, characteristic function

JEL Classification: G12, G13