Implicit Volatility and the Pricing of Stock Index and Interest Rate Options in US Markets

The Black‐Scholes (B‐S) model in its various formulations has been the mainstay paradigm on option pricing since its basic formulation in 1973. The model has generally been proven empirically robust, despite the well documented empirical evidence of mispricing deep‐in‐the‐money, deep out‐of‐the‐money and, occasionally, at‐the‐money options with near maturities [see Galai (1983)]. Research on explaining the observed pricing anomalies has focused on the variance of the return of the underlying asset, which, in the case of the B‐S model, is assumed to remain invariant over time. The variance term is not directly observable, leading researchers to speculate that pricing discrepancies may be caused by misspecification of this variable. More specifically, interest in the volatility variable has centered about the implied standard deviation (ISD).