Pricing Vulnerable Options With Variance Gamma Systematic and Idiosyncratic Factors by Laplace Transform Inversion

Abstract

This paper studies the pricing of vulnerable options with systematic and idiosyncratic factors incorporated. Variance gamma processes are employed to model price jumps caused by the arrivals of systematic and idiosyncratic relevant information. A parsimonious pricing measure is developed and Laplace transforms of option price and Greek letters are given. Numerical results are obtained by a two-sided Euler inversion method in an efficient and accuracy way. It shows that in contrast to idiosyncratic factors, the effect of systematic factors on vulnerable options is strongly affected by the skewness and leptokurtosis features of systematic variance gamma processes.