The Black-Scholes option pricing formula assumes that the variance of the return on the underlying stock is known with certainty. In practice an estimate of the variance, based on a sample of historical stock prices, is used. The estimation error in the variance induces error in the option price. Since the option price is a nonlinear function of the variance, an unbiased estimate of the variance does not produce an unbiased estimate of the option price. For reasonable parameter values, it is shown that the magnitude of the bias is not large.