Explaining the level of credit spreads: option-implied jump risk premia in a firm value model

BIS Working Papers No 191
November 2005
On 9-10 September 2004, the BIS held a workshop on The pricing of credit risk. This event brought together central bankers, academics and market practitioners to exchange views on this issue (see the conference programme in this document). This paper was presented at the workshop. The views expressed are those of the author(s) and not those of the BIS.

Abstract:

Prices of equity index put options contain information on the price of systematic downward jump risk. We use a structural jump-diffusion firm value model to assess the level of credit spreads that is generated by option-implied jump risk premia. In our compound option pricing model, an equity index option is an option on a portfolio of call options on the underlying firm values. We calibrate the model parameters to historical information on default risk, the equity premium and equity return distribution, and S&P 500 index option prices. Our results show that a model without jumps fails to fit the equity return distribution and option prices, and generates a low out-of-sample prediction for credit spreads. Adding jumps and jump risk premia improves the fit of the model in terms of equity and option characteristics considerably and brings predicted credit spread levels much closer to observed levels.

JEL classification: G12, G13

Keywords: credit spreads, firm value model, jump-diffusion model, option pricing