Contingent Claim Pricing Using the Cauchy Probability Distortion Operator under Simple Transformation

The problem of pricing contingent claims has beenextensively studied for non-Gaussian models, and in particular,Black- Scholes formula has been derived for the NIG assetpricing model. This approach was first developed in insurancepricing where the original distortion function was defined interms of the normal distribution.This approach was later studied to compare the standardBlack-Scholes contingent pricing and distortion basedcontingent pricing. In this paper, we aim at using distortionoperators by Cauchy distribution under a simpletransformation to price contingent claim. We also show that wecan recuperate the Black-Sholes formula using the distribution.