A Double Exponential Jump Diffusion Process to Modelling Risky Bond Prices

Abstract

This paper aims at providing an extension of Zhou [1997] and Black and Cox [1976] by considering the case where the default can occur at any time and the asset value dynamics is modelled by a jump diffusion process. This extension is provided by considering a special case of jump diffusion process. Following Kou and Wang [2001,2003], Lipton [2002] and Sepp [2003], we consider that the log jump sizes are random variables double asymmetric exponentially distributed. Thanks to this particular choice, quasi-explicit formula is available for the joint probability of the first passage time and the terminal value. We characterized the price of the risky bond and derived a closed form in Laplace domain. Black and Cox [1976], Zhou [1997] models and this model have been implemented and numerically compared.