Comparative Evaluation of Predictive Accuracy of the Linear Black–Scholes Model and Nonlinear Heston and Quantum Schrödinger Models in Option Pricing in the Tehran Stock Exchange

Abstract

This study aims to comparatively evaluate the predictive accuracy of three option pricing models—Black–Scholes, Heston, and Quantum Schrödinger—to determine the most reliable valuation framework for the volatile conditions of Iran’s derivatives market. This applied quantitative research employed real data from European call options traded on the Tehran Stock Exchange between 2016 and 2022. The Black–Scholes, Heston, and Schrödinger models were implemented and calibrated in Python 3.9 using finite difference and fourth-order Runge–Kutta numerical schemes. Performance accuracy was assessed through RMSE, MAE, and R² indices, and sensitivity to risk-free interest rate variations was examined. The results revealed that the quantum Schrödinger model achieved the lowest prediction error (RMSE = 26.968) and the highest coefficient of determination (R² = 0.6879), outperforming both the Heston model (RMSE = 65.029, R² = 0.6537) and the Black–Scholes model (RMSE = 767.292, R² = 0.5091). Nonlinear adaptive models demonstrated significantly superior accuracy in replicating the dynamic behavior of Iran’s volatile derivatives market compared to traditional linear frameworks. The study concludes that the nonlinear quantum Schrödinger model is the most accurate and robust framework for option pricing in the Tehran Stock Exchange. Its application can enhance risk management precision, improve market transparency, and optimize derivative valuation strategies in emerging financial markets.