The hybrid pareto distribution, implied risk-neutral density and option pricing

Abstract

This paper aims to develop a new European option pricing model based on the Extreme Value Theory (EVT). We assume that, in the risk-neutral probability measure, simple negative returns of the S&P500 index follow the Hybrid Pareto (HP) distribution. Then, we derive closed-form pricing formulas for call and put options according to the risk-neutral pricing method. Additionally, we assume that the distribution has a fat tail. Our study’s benchmark model is the Generalized Extreme Value (GEV) model proposed by Markose and Alenton (2011). We estimate model parameters by minimizing the root-mean-square error. The results show that the HP model provides less root-mean-square errors than the GEV model in a 30-day to expiration options. Moreover, it outperforms the benchmark for the at-the-money options, but has a poorer fit for the out-of-the-money options.