Unbiased Estimation of Option Prices: An Examination of the Return From Hedging Options Against Stocks

Abstract:     
In this paper we examine the effect of bias in option price estimates on the estimated returns from hedging options against stocks. The source of bias examined here is the estimation bias introduced from inserting an estimate of asset volatility into an option-pricing formula. This source of bias has been documented in a number of theoretical studies. To empirically evaluate the effect of estimation bias in option price estimates we use the unbiased option price estimator of Butler and Schachter (1986) and an unbiased estimator of the option hedge ratio. We identify four mutually exclusive and exhaustive cases for the effect of estimation bias on calculated option hedge returns. We find the returns on portfolios of mispriced options are very similar whether we use biased or unbiased estimates of option prices and option hedge ratios, indicating that the effects of estimation biases are, for the most part, smaller than other sources of "noise" in the data.

JEL Classification: G13

Accepted Paper Series