Dynamic Hedging and Volatility Expectation 166 6. Dynamic Hedging and Volatility Expectation Summary: The implied volatility derived from inverting the Black-Scholes equation to solve for the price of an option is not an unconditional forecast
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چکیده
The implied volatility derived from inverting the Black-Scholes equation to solve for the price of an option is not an unconditional forecast of future volatility (unless volatility is deterministic). It is only a forecast of the square root of the average variance of a biased set of sample paths for the underlying security –those paths that will affect the dynamic hedging of the option. Most research papers testing the “rationality” of the volatility implied from option prices naïvely miss the point. We compute the error to be large enough to invalidate a large number of empirical tests in the literature. An unconditional variance contract is created that is an unbiased rational predictor of future variance, and the properties of an accurate replicating portfolio are shown.
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