An Empirical Test of the Black-Scholes Option Pricing Model and the Implied Variance: A Confidence Interval Approach

The empirical studies on the Black-Scholes (B-S) option pricing model have reported that the model tends to exhibit systematic biases with respect to the exercise price, time to expiration, and the stock's volatility. This paper attempts to test the B-S model with a new approach: derive the confidence interval of the model call option value based on the confidence interval of the. estimated variance. The test reports that even when the variance's confidence interval is considered, a systematic deviation between the theoretical “range” of the option price values and the observed market price still exist. If the stock variance is constant over time, the interpretation of the results is that the B-S model is wrong. However, if stock variance changes over time, the interpretation of the results is that the implied volatility in options market prices had a tendency to be significantly higher than the estimate that could have been obtained from historical data.