Implied Volatility Functions: Empirical Tests
Black and Scholes (1973) implied volatilities tend to be systematically related to the option’s exercise price and time to expiration. Derman and Kani (1994), Dupire (1994), and Rubinstein (1994) attribute this behaviour to the fact that the Black/Scholes constant volatility assumption is violated in practice. These authors hypothesize that the volatility of the underlying asset’s return is a deterministic function of the asset price and time, and develop the deterministic volatility function (DVF) option valuation model, which has the potential of fitting the observed cross-section of option prices exactly. Using a sample of Standard and Poors index of 500 companies (S&P 500) options during the period June 1988 through December 1993, we evaluate the economic significance of the implied deterministic volatility function by examining the predictive and hedging performance of the DVF option valuation model.
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