Jump diffusion in credit barrier modeling: a partial integro-differential equation approach

Abstract

The credit migration process contains important information about the dynamics of a firm's credit quality, therefore, it has a significant impact on its relevant credit derivatives. We present a jump diffusion approach to model the credit rating transitions which leads to a partial integro-differential equation (PIDE) formulation, with defaults and rating changes characterized by barrier crossings. Efficient and reliable numerical solutions are developed for the variable coefficient equation that result in good agreement with historical and market data, across all credit ratings. A simple adjustment in the credit index drift converts the model to be used in the risk-neutral setting, which makes it a valuable tool in credit derivative pricing.

Citation

Zhu, J. (2008), "Jump diffusion in credit barrier modeling: a partial integro-differential equation approach", Fouque, J.-P., Fomby, T.B. and Solna, K. (Ed.) Econometrics and Risk Management (Advances in Econometrics, Vol. 22), Emerald Group Publishing Limited, Leeds, pp. 195-214. https://doi.org/10.1016/S0731-9053(08)22008-6