Mispricing in the Black-Scholes model: an exploratory analysis

The Black-Scholes option pricing model has been highly influential in security trading and in analyses of risk-price relationships, despite the fact that it has been shown to have an apparent unexplainable mispricing bias. This study examines the mispricing exhibited by the Black-Scholes model and shows that it can be explained by the estimation procedures utilized and the measures of volatility. Specifically, a model is constructed to test for the systematic over- or underpricing of the Black-Scholes model. Striking price and time-to-maturity are included in the model. The model also includes an autoregressive error structure. Recognizing the autocorrelation in the errors improves estimation efficiency and predictability of future option prices. The method of entering implied volatility into the model has a great impact. When only one estimated implied volatility was used to explain the option data, the Black-Scholes model exhibited a bias that was a similar function of striking price for all of the securities studied. When separate estimated implied volatilities for different option positions were used, the bias as a function of striking price and time-to-maturity varied among securities. Predictions of market option prices based on the model containing striking price, time-to-maturity, and an autoregressive error structure were more accurate than those based on the Black-Scholes model.