Stochastic Volatility Effects on Defaultable Bonds

Abstract

This paper studies the effect of introducing stochastic volatility in the first‐passage structural approach to default risk. The impact of volatility time scales on the yield spread curve is analyzed. In particular it is shown that the presence of a short time scale in the volatility raises the yield spreads at short maturities. It is argued that combining first passage default modelling with multiscale stochastic volatility produces more realistic yield spreads. Moreover, this framework enables the use of perturbation techniques to derive explicit approximations which facilitate the complicated issue of calibration of parameters.

Keywords:

• First‐passage structural approach
• stochastic volatility
• time scales
• yield spreads
• calibration

Acknowledgements

This work was supported by NSF grant DMS0455982 (J‐P F.) and partially supported by NSF grants DMS 0306357 and DMS 0456195 (R.S), and the Sloan Foundation (K.S.).