The Efficacy of the Black–Scholes Option Pricing Model in Valuing Nifty 50 Single Stock Options: Is There a Difference Between Shariah-Compliant and Non-Compliant Constituent Stocks?

Abstract

This study investigates the pricing efficacy of single-stock options on India's NIFTY 50 index by applying the Black–Scholes Option Pricing Model (BSOPM) to both call and put options from December 18, 2024–January 30, 2025. Theoretical prices were estimated using standard inputs (spot, strike, volatility, time to maturity, and a 5.98 % risk-free rate), and mispricing was defined as the difference between market prices and theoretical prices. Paired t-tests and Welch’s tests compared overall mispricing and segmental differences between Shariah-compliant and conventional stocks. The findings revealed widespread mispricing: 46.9% of call options and 57.14% of put options exhibit significant underpricing relative to theoretical values. However, contrary to expectations that Shariah-compliant stocks might display different pricing behaviour due to structural characteristics like lower leverage and volatility, no statistically significant difference in mispricing was observed between Shariah-compliant and conventional options. These results suggest that broader market factors—such as liquidity, risk aversion, and regulatory dynamics—play a more dominant role in influencing pricing inefficiencies than the Shariah compliance of the underlying stocks. These insights can guide hedging strategies for institutional investors and inform regulatory oversight in emerging derivatives markets.