Default risk in interest rate derivatives with stochastic volatility

Abstract

In this study, we consider short interest rate models of the Vascicek type with stochastic volatility and obtain formulas for default risk in interest rate derivatives. Corrections from a fast mean-reverting stochastic volatility are computed to show how they can affect the term structure of the interest rate derivatives. Our results for the defaultable bonds as well as the corresponding bond options are obtained as an extension of the non-defaultable case studied by Cotton et al. [Math. Finance, 2004, 14(2), 173–200].

Keywords:

• Applications to default risk
• Applied mathematical finance
• Stochastic interest rates
• Term structure
• Volatility modelling
• Arbitrage pricing

Acknowledgements

The authors thank the anonymous referees for useful suggestions. This work was supported by the Brain Korea 21 project 2007 (B.K.) and by Korea Research Foundation grant KRF-2008-314-C00045 (J.-H.K.).