A Simulation Analysis of Distortion Operators of Wang, NIG and Cauchy: A Comparative Approach

The problem of pricing contingent claims has been extensively studied for non-Gaussian models and in particular, Black- Scholes formula has been derived for the NIG asset pricing model. This approach was originally studied in Insurance pricing where the distortion function was defined in terms of the normal distribution. It was also used to compare the standard Black-Scholes contingent pricing and distortion based contingent pricing. So, in this paper, we aim at using the Cauchy simulation analysis via MATLAB to compare the Wang distortion and NIG distortion operator with their pricing model. The results show that we can recuperate the Black-Scholes and NIG pricing model using the simulation of Cauchy distortion operator.