Unbiased estimation of the Black/Scholes formula

The Black/Scholes model gives the price of an option as a function of the true variance rate of the underlying stock and other parameters. Because the true variance rate is unobservable, an estimate of the variance rate is used in empirical tests. But, because the Black/Scholes formula is non-linear in the variance, option price estimates using an estimated variance are biased, even if the variance estimate itself is unbiased. This paper develops an unbiased estimator of the Black/Scholes formula from a Taylor series expansion of the formula and the properties of the pdf of the estimated variance.