Pricing Options On Defaultable Stocks Under A Multiscale Intensity Model

We introduce the model of credit risk in this paper,and the Intensity model is usedto derive the corresponding option pricing formula of defaultable stocks. The modelwe proposed is a optimized form of intensity-based models. The model characterizesthe default risk all sidedly,which takes both the intensity of default and the stochasticvolatility into account. The intensity of defaults is also assumed to be in?uenced bythe volatility. We use regular and singular perturbation expansions on analysing theintensity of default and the stochastic volatility,and we consider that they are bothdecided by a two-factor diffusion.It is shown that an effective hazard rate from bonds issued by a company canbe used to explain the implied volatility skew of the option prices issued by the samecompany. And it might be possible to infer the risk neutral default intensity from thestock option prices. It is observed that the seven-parameter-model we proposed hasa rich implied volatility surface structure and fits the data of implied volatility well.Besides,the implied yield spread obtained from calibrating all the model parameters tothe option prices matches the observed yield spread well.