derive the IV's from a Binomial model that captures the value of early exercise. This resolves the problem of analyzing American options, but does not address the many other issues raised by the possibility that the "market" may not be using exactly the same model we are. For example, the market's option model may allow nonlognormal price changes or price jumps. Using the wrong model violates (3): the computed IV will not be the market's real volatility forecast. In the early studies, stock price volatility was typically treated as if it were a constant parameter, so that the exact timing and periodicity of the data sample used in estimating it did not matter much. Problems included use of sparse monthly data spanning long time periods to estimate historical volatility, estimating "realized" volatility over periods that did not match option maturity, and in at least one case, analyzing "forecasts" of volatility over periods prior to the date the forecast was made. Only Beckers was fully sensitive to the importance of timing, using daily data to estimate historical volatility from the previous three months of stock prices, and realized volatility over the period from the observation date to option expiration. A major problem affecting all empirical analysis of implied volatility is that it must be computed from market prices that are "noisy." Two reasons for noise are the bid-ask spread and nonsynchronous trading. Since IV calculations are based on recorded transactions prices and there is a spread between the market's bid and offer for both the stock and the option, the IV will be affected by whether the last trades resulted from market buy or sell orders. Also, with daily data the trades producing the recorded closing prices may have occurred at different times, which introduces additional noise. All of the studies we have mentioned, as well as the present paper, suffer from these problems. They should be more severe for stocks and options with wide bid-ask spreads and those that trade relatively infrequently. We expect noise to be of lesser importance, though still present, for actively traded options on a broad stock index like the OEX. The existence of noise in computing IV causes a violation of equation (3): The measured IV is
derive the IV's from a Binomial model that captures the value of early exercise. This resolves the problem of analyzing American options, but does not address the many other issues raised by the possibility that the "market" may not be using exactly the same model we are. For example, the market's option model may allow nonlognormal price changes or price jumps. Using the wrong model violates (3): the computed IV will not be the market's real volatility forecast. In the early studies, stock price volatility was typically treated as if it were a constant parameter, so that the exact timing and periodicity of the data sample used in estimating it did not matter much. Problems included use of sparse monthly data spanning long time periods to estimate historical volatility, estimating "realized" volatility over periods that did not match option maturity, and in at least one case, analyzing "forecasts" of volatility over periods prior to the date the forecast was made. Only Beckers was fully sensitive to the importance of timing, using daily data to estimate historical volatility from the previous three months of stock prices, and realized volatility over the period from the observation date to option expiration. A major problem affecting all empirical analysis of implied volatility is that it must be computed from market prices that are "noisy." Two reasons for noise are the bid-ask spread and nonsynchronous trading. Since IV calculations are based on recorded transactions prices and there is a spread between the market's bid and offer for both the stock and the option, the IV will be affected by whether the last trades resulted from market buy or sell orders. Also, with daily data the trades producing the recorded closing prices may have occurred at different times, which introduces additional noise. All of the studies we have mentioned, as well as the present paper, suffer from these problems. They should be more severe for stocks and options with wide bid-ask spreads and those that trade relatively infrequently. We expect noise to be of lesser importance, though still present, for actively traded options on a broad stock index like the OEX. The existence of noise in computing IV causes a violation of equation (3): The measured IV is
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