Paper: arXiv 2508.14577

Authors: Tapan Kar, Suprio Bhar, Barun Sarkar, Sesha Meka

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.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 6.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a rigorous mathematical derivation of option pricing using Pearson diffusion processes, including explicit verification of the Novikov condition for risk-neutral pricing. It validates the framework empirically against Black-Scholes and Heston models on Nifty 50 index options, demonstrating superior performance, though full reproducibility is slightly constrained by the absence of explicit code links.

Research Flowchart

  flowchart TD
    A[Goal: Enhance Option Pricing via Pearson Diffusion Processes] --> B[Theoretical Framework: Model Returns with Linear Drift & Quadratic Diffusion]
    B --> C[Risk-Neutral Validation: Verify Novikov Condition & Strong Solution]
    D[Input Data: Nifty 50 Index Option Data] --> E[Empirical Calibration & Model Comparison]
    C --> E
    F[Benchmarks: Black-Scholes & Heston Models] --> E
    E --> G[Outcome: Superior Pricing Accuracy Capturing Skewness & Kurtosis]