This paper seeks to investigate the degree of mispricing in the Black-Scholes call options pricing model. The aim is to research if the degree of mispricing in the Black-Scholes model has increased or decreased, from a historical perspective.
Our hypothesis is that with a large increase in option trading volume and a larger participation of retail investors, might have an impact on the option pricing. Thus, indirectly affecting the Black-Scholes pricing model — which we seek to investigate, if such changes have led to less efficiency in the model today.
The Black-Scholes model, introduced in 1973, revolutionized financial markets by providing the first widely-adopted framework for pricing European-style options. Its elegant mathematical formulation — based on assumptions of constant volatility, log-normal price distributions, and frictionless markets — became the foundation of modern derivatives trading.
However, the market environment has changed dramatically since the model's inception. The proliferation of commission-free trading platforms, the rise of retail options speculation, and the increasing influence of social media on trading behavior have fundamentally altered market microstructure.
Using a dataset of S&P 500 index options spanning from 2005 to 2024, we compare Black-Scholes theoretical prices against observed market prices across different moneyness levels and expiration horizons. Our analysis reveals a statistically significant increase in mispricing since 2020, particularly for short-dated, out-of-the-money call options.
These findings suggest that the assumptions underlying the Black-Scholes model are increasingly misaligned with contemporary market dynamics, and that the influx of retail participation has introduced pricing inefficiencies that the model fails to capture. We discuss implications for risk management, market makers, and the development of alternative pricing frameworks.
