Contingent Claim Pricing Using a Normal Inverse Gaussian Probability Distortion Operator

Abstract

We consider the problem of pricing contingent claims using distortion operators. This approach was first developed in (Wang, 2000) where the original distortion function was defined in terms of the normal distribution. Here, we introduce a new distortion based on the Normal Inverse Gaussian (NIG) distribution. The NIG is a generalization of the normal distribution that allows for heavier skewed tails. The resulting operator asymmetrically distorts the underlying distribution. Moreover, we show how we can recuperate non-Gaussian Black-Scholes formulas using distortion operators and we provide illustrations of their performance. We conclude with a brief discussion on risk management applications. © The Journal of Risk and Insurance, 2012.