A three-factor hazard rate model for single-name credit default swap pricing

Yangfan Zhong and Yanhui Mi

Abstract

We propose a reduced-form model that integrates the modeling of interest rates, equity and default hazard rates. In this model the evolution of the risk-neutral hazard rate is driven by three risk factors: the reference firm’s equity price (in logarithmic form), the risk-free short rate and a latent risk premium factor that is orthogonal to the first two. The equity price and the short rate are considered to be the two primary risk factors, while the risk premium factor is introduced to capture the remaining risks for the hazard rate (such as the liquidity risk). The equity price follows a diffusion process with the possibility of a jump to default, the short rate is governed by a Vasicek model, and the dynamics of the risk premium factor are modeled as a Cox– Ingersoll–Ross process. Under the three-factor model, we derive computable pricing formulas for defaultable zero-coupon bonds, European call options and standard running credit default swaps (CDSs).We then discuss the calibration of the model using CDS and equity option data. Our numerical results reveal that the model is able to interpret a diverse set of CDS spread term structures.