Call Option Price using Pearson Diffusion Processes

TL;DR

This paper proposes a new option pricing model using Pearson diffusion processes that better capture empirical return features like skewness and kurtosis, validated through real market data and outperforming classical models.

Contribution

It introduces a novel Pearson diffusion-based framework for option pricing, ensuring no arbitrage and demonstrating superior empirical performance over Black--Scholes and Heston models.

Findings

Model captures skewness and kurtosis of returns.

Outperforms Black--Scholes and Heston models on Nifty 50 data.

Ensures no arbitrage via Novikov condition.

Abstract

Following the foundational work of the Black--Scholes model, extensive research has been developed to price the option by addressing its underlying assumptions and associated pricing biases. This study introduces a novel framework for pricing European call options by modeling the underlying asset's return dynamics using Pearson diffusion processes, characterized by a linear drift and a quadratic squared diffusion coefficient. This class of diffusion processes offers a key advantage in its ability to capture the skewness and excess kurtosis of the return distribution, well-documented empirical features of financial returns. We also establish the validity of the risk-neutral measure by verifying the Novikov condition, thereby ensuring that the model does not admit arbitrage opportunities. Further, we study the existence of a unique strong solution of stock prices under the risk-neutral measure. We apply the proposed method to Nifty 50 index option data and conduct a comparative analysis against the classical Black--Scholes and Heston stochastic volatility models. Results indicate that our method shows superior performance compared to the other two benchmark models. These results carry practical implications for market participants, including market makers, hedge funds, and derivative traders.