Analytical valuation of vulnerable European and Asian options in intensity-based models

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. •We investigate vulnerable European and Asian options in an intensity-based model.•The underlying asset price is described by a two-factor stochastic volatility model.•The correlation between the underlying asset and default risk is incorporated.•We obtain explicit pricing formulae of vulnerable European and Asian options.•The effects of default risk and systematic risk on option prices are illustrated.