Beyond Black-Scholes: Evidence of Systematic Mispricing in the Indian Options Market and the Case for a Behavioral Pricing Model
DOI:
https://doi.org/10.66635/9xbvc809Keywords:
Black-Scholes model, Option mispricing, Moneyness, Probability weighting, Indian derivatives marketAbstract
This study examines whether Black-Scholes option prices deviate systematically from observed market prices in the Indian equity derivatives market, and whether the pattern of deviation supports a behavioral interpretation. Black-Scholes theoretical prices were computed for 69,372 call-option observations across 47 Nifty-50 constituent stocks between January 2023 and December 2024. Pricing errors were tested company-wise and in aggregate using paired-sample and one-sample t-tests, and compared across moneyness categories using the Friedman test with Kendall’s coefficient of concordance. Because pricing errors are strongly serially correlated, all inference is reported both naively and with Newey-West HAC standard errors, cluster-level aggregation and false discovery rate control, with effect sizes accompanying every test. Black-Scholes prices differ significantly from market prices, with a median absolute error of 18.9 percent of premium, although the effect size is small. The direction of deviation is not stable: market prices were below the model prices in 2023 and above them in 2024, and the sign tracks the annual volatility input rather than investor behavior, so no behavioral reading of the direction is defensible. The robust finding concerns magnitude. Using moneyness reconstructed from contemporaneous strike-to-spot ratios, median absolute percentage error is 4.6 percent for in-the-money contracts, 21.5 percent for at-the-money contracts and 70.1 percent for out-of-the-money contracts. Every one of the 47 companies displays this ordering, and it holds within each year of the sample separately. Relative mispricing therefore concentrates in the segment whose value depends entirely on small-probability outcomes, which points toward probability weighting rather than loss aversion as the mechanism most likely to carry explanatory power in this market. The study further documents that where volatility is estimated annually rather than implied from contract prices, the direction of measured mispricing follows that input, a result bearing on how existing Indian evidence on the sign of Black-Scholes error should be interpreted.
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