Valuing fade-in options with default risk in Heston–Nandi GARCH models

In this paper, we present a pricing model to value fade-in options with default risk, where the underlying asset price is driven by the Heston–Nandi GARCH process and is correlated with the intensity process. The explicit pricing formulae are obtained, which contain pricing formulae of vanilla European options with/without default risk as special cases. Finally, a comparative analysis of the impacts of default risk is provided.