Default Distances Based on the CEV-KMV Model

Abstract

This paper presents a new method to assess default risk based on applying the CEV process to the KMV model. We find that the volatility of the firm asset value may not be a constant, so we assume the firm's asset value dynamics are given by the CEV process $\frac{dV_A}{V_A} = \mu_A dt + \delta V_A^{\beta-1}dB$ and use the equivalent volatility method to estimate parameters. Focus on the distances to default, our CEV-KMV model fits the market better when forecasting the credit risk compared to the classical KMV model. Besides, The estimation results show the $\beta>1$ for non ST companies while $\beta<1$ for ST companies, which means their difference in the local volatility structure: ST volatility is decreasing with respect to the firm's asset while non ST volatility is increasing.