In this paper, we investigate European and Asian options with default risk in an intensity-based model. By breaking down the risk into idiosyncratic and systematic components, we describe the underlying asset price using a two-factor stochastic volatility model and incorporate the correlation between the underlying asset and default risk. In the proposed framework, we obtain explicit pricing formulae of European and Asian options with default risk and illustrate the effects of default risk and systematic risk on option prices. Specially, prices of the options with default risk increase with systematic risk. By contrast, prices of the options with default risk drop as systematic risk increases when we keep the total initial volatility of the underlying asset unchanged.

在本文中，我们在基于强度的模型中调查了具有违约风险的欧洲和亚洲期权。通过将风险分解为特殊的和系统的组成部分，我们使用两因素随机波动率模型描述了基础资产价格，并纳入了基础资产和违约风险之间的相关性。在提出的框架中，我们获得了带有违约风险的欧洲和亚洲期权的明确定价公式，并说明了违约风险和系统风险对期权价格的影响。特别是，具有默认风险的期权价格会随着系统性风险而增加。相反，当我们保持标的资产的总初始波动率不变时，具有违约风险的期权价格会随着系统性风险的增加而下降。