Pricing Options on Defaultable Stocks
by Erhan Bayraktar of the University of Michigan
Abstract: We develop stock option price approximations for a model which takes both the risk of 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 option prices issued by the same company. We also observe that the implied yield spread that is obtained from calibrating all the model parameters to the option prices matches the observed yield spread.
Keywords: Option pricing, multiscale perturbationmethods, defaultable stocks, stochastic intensity of default, implied volatility skew.
Published in: Applied Mathematical Finance, Vol. 15, No. 3, (June 2008), pp. 277-304.
Previously titled: A Note on Pricing Options on Defaultable Stocks