Valuation of vulnerable options using a bivariate Gram–Charlier approximation

In this paper, we focus on vulnerable options using the bivariate Gram–Charlier approximation, rather than any specific stochastic processes as in previous studies on vulnerable options. After deriving a closed-form pricing formula of vulnerable options, we perform numerical examples to illustrate the effects of the (co)skewness and excess (co)kurtosis parameters. Numerical results show that the skewness (excess kurtosis) parameters of the underlying asset and the issuer’s assets have opposite effects on vulnerable option prices. Specially, all the counterintuitive observations are explained by emphasizing the role of the risk compensation item.