Distance to default based on the CEV–KMV model

Wen Su

Abstract

This paper presents a new method with which to assess default risk based on applying the constant elasticity of variance (CEV) process to the Kealhofer-McQuown-Vasicek (KMV) model. We find that the volatility of the firm’s asset value may not be a constant, so we assume that the firm’s asset value dynamics are given by the CEV process dV_A/V_A=μ_Adt+δ V_A^β−1dB and use the equivalent volatility method to estimate the parameters. In terms of distance to default, our CEV-KMV model fits the market better when forecasting credit risk compared with the classical KMV model. Moreover, the estimation results show that β>1 for non-special treatment (non-ST) companies and that β<1 for special treatment (ST) companies, which shows their difference with respect to the firm’s assets in the local volatility structure: ST volatility decreases while non-ST volatility increases.