Pricing Options on Defaultable Stocks

TL;DR

This paper develops a model for pricing stock options considering default risk and stochastic volatility, showing how implied volatility surfaces can be effectively approximated and linked to bond hazard rates.

Contribution

It introduces a new approximation method for option prices that incorporates default risk and stochastic volatility, and demonstrates how to infer default intensity from option prices.

Findings

Option price approximation captures rich implied volatility surface.

Calibration links bond hazard rates to implied volatility skew.

Model fits market data well.

Abstract

In this note, we develop stock option price approximations for a model which takes both the risk o default and the stochastic volatility into account. We also let the intensity of defaults be influenced by the volatility. We show that it might be possible to infer the risk neutral default intensity from the stock option prices. Our option price approximation has a rich implied volatility surface structure and fits the data implied volatility well. Our calibration exercise shows that an effective hazard rate from bonds issued by a company can be used to explain the implied volatility skew of the implied volatility of the option prices issued by the same company.