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A Structural Credit Risk Model with Stochastic Volatility and Jumps
A firm's debt valuation model that takes into account stochastic volatility, jumps and interest rate risks is developed in this paper. Semi-closed formulas are obtained for the credit risk measures of the firm's risky debt in a double exponential jump-diffusion model with stochastic volatility and stochastic interest rate using the Fourier transform technique. We compared the credit spread term structure of our proposed model with those of other models, including the classical structural model and the double exponential jump-diffusion model. At last, we analyzed several effects of both stochastic volatility and interest rate on credit spread term structure under the proposed model. Computational experiments show that incorporating both stochastic volatility and jumps into the firm's value can substantially increases the values of the credit spreads. The proposed model is very useful for empirical analysis of asset returns and managing the firm credit risks.
Risky debts, jump-diffusion model, stochastic volatility, Fourier transform technique.
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