Abstract—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 first developed in insurance pricing where the original distortion function was defined in terms of the normal distribution.
This approach was later studied to compare the standard Black-Scholes contingent pricing and distortion based contingent pricing. In this paper, we aim at using distortion operators by Cauchy distribution under a simple transformation to price contingent claim. We also show that we can recuperate the Black-Sholes formula using the distribution.

Index Terms—Wang transformation, NIG and cauchy distribution under a simple transformation, distortion operator, contingent pricing.

The authors are with the Department of Mathematics, Abia State University, Uturu, P. M. B.2000. Nigeria. (e-mail:megaobrait@yahoo.com).

Cite: Bright O. Osu and Godswill U. Achi, "Contingent Claim Pricing Using the Cauchy Probability Distortion Operator under Simple Transformation," International Journal of Applied Physics and Mathematics  vol. 3, no. 1, pp. 8-13, 2013.