The statistical properties of parameters inferred from the Black-Scholes formula

A large body of literature investigates various issues by using parameters inferred from the Black-Scholes formula. Little of this research conducts statistical tests of hypotheses, because the distributional properties of inferred parameters are unknown. As a result, conclusions are frequently reached based solely on economic significance. Discussions of economic significance are insufficient to draw conclusions when statistical significance is unknown. This paper presents a technique for deriving the distributional properties of inferred parameters and discusses the manner in which this information can be used to construct hypothesis tests. This paper also provides a rationale for the empirically observed superiority of ISDs obtained from at-the-money options. The results indicate that parameters inferred singly tend to have desirable properties. However, multiple-parameter estimates obtained simultaneously from option prices can be subject to substantial error if even one of the options used is not near the money.