A Simulation Analysis of Distortion Operators of Wang, NIG and Cauchy: A Comparative Approach
Godswill U. Achi *
Department of Mathematics and Statistics, School of Science, Akanu Ibiam Federal Polytechnic, Uwana, Afikpo, Nigeria.
Francis A. Ujah
Department of Mathematics and Statistics, School of Science, Akanu Ibiam Federal Polytechnic, Uwana, Afikpo, Nigeria.
Sambo Dachollom
Department of Mathematics and Statistics, School of Science, Akanu Ibiam Federal Polytechnic, Uwana, Afikpo, Nigeria.
*Author to whom correspondence should be addressed.
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 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.
Keywords: Wang distortion operator, NIG, Cauchy distortion operator and simulation analysis.