On the Risk Neutralization of Transition Matrix

Abstract

Risk-neutral transition matrix term structure is an essential component of rating-based credit derivative pricing models. However, generation of suitable risk-neutral transition matrix term structure remains a challenging problem. Many calibration models in the literature either are unstable or result in poor fit to the market implied default probability term structure.In this paper, we propose a new risk-neutral transition matrix term structure calibration method in which the conditional rating transition matrix is a mixture of Markov chains. Numerical results indicate that the local Markov mixture model is capable of accurately calibrating to a variety of market implied CDS/PD term structure.