Credit Spreads and State-Dependent Volatility : Theory and Empirical Evidence

We generalize the asset dynamics assumptions of Leland (1994b) and Leland and Toft (1996) to a much richer class of models. By assuming a stationary corporate debt structure with constant principal, coupon payment and average maturity through continuous retirement and refinancing as long as the firm remains solvent, we obtain analytical solutions with the state dependent diffusion volatility following the constant elasticity of variance (CEV) process for the variables of interest, including corporate debt value, total levered firm value and equity value. We then apply our derivations to time-series data extracted from a sample of firms, extract the models' parameters and compare the performance of our CEV model to the constant volatility (zero elasticity) assumption of earlier studies. We find that the elasticity is significantly different from zero for most of the firms in our sample, and that the CEV model performs much better than constant volatility in predicting CDS spreads, especially with respect to the medium and long-term spreads