Call Option Price using Pearson Diffusion Processes

This study introduces a framework for pricing European call options using Pearson diffusion processes with linear drift and quadratic squared diffusion. This class of diffusion processes follows Pearson type IV distribution as its invariant distribution which can effectively capture skewness and excess kurtosis, key empirical features of financial returns. We verify the Novikov condition for risk-neutral measure, and establish the existence of a unique strong solution of stock prices under this measure. We apply the method to Nifty 50 index options and find encouraging results compared to the Black-Scholes and Heston models.