Weisbach are gratefully acknowledged. I bear full responsibility for all remaining errors. Forecasting Future Volatility from Option Prices Evidence exists that option prices produce biased forecasts of future volatility across a wide variety of options markets. This paper presents two main results. First, approximately half of the forecasting bias in the S&P 500 index (SPX) options market is eliminated by constructing measures of realized volatility from five minute observations on SPX futures rather than from daily closing SPX levels. Second, much of the remaining forecasting bias is eliminated by employing an option pricing model that permits a non-zero market price of volatility risk. It is widely believed that option prices provide the best forecasts of the future volatility of the assets which underlie them. One reason for this belief is that option prices have the ability to impound all publicly available information – including all information contained in the history of past prices – about the future volatility of the underlying assets. A second related reason is that option pricing theory maintains that if an option prices fails to embody optimal forecasts of the future volatility of the underlying asset, a profitable trading strategy should be available whose implementation would push the option price to the level that reflects the best possible forecast of future volatility.

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Academics and practitioners have substantial interest in the implied volatility patterns recovered from commodity futures options. Such knowledge enhances their ability to accurately forecast volatility embedded in these high-risk options. This paper reviews option-implied volatility in the September corn futures option contracts for the period of 1991-2000. It also investigates whether a "weekend effect" exists. We compare forecasting performance of different historical volatility measures. We further report average trading profits of a short straddle strategy, which is motivated by differences between option implied volatility and historical volatility. JEL Code: G10, G12, G13 Keywords: commodity futures options, implied volatility 1.

Although it is widely believed that option prices provide the best possible forecasts of the future variance of the assets which underlie them, a large body of empirical evidence concludes that option prices consistently yield biased forecasts of future variance. The prevailing interpretation of these findings is that option investors may be forming unbiased forecasts of the future variance of underlying assets but that these unbiased forecasts fail to get impounded into option prices because of either (1) the difficulty of carrying out the necessary arbitrage strategies that would force the prices to their proper levels, or (2) the availability to market makers of lucrative alternative strategies in which they simply profit from the large bid-ask spreads in the options markets. This interpretation has significant consequences for nearly the entire range of option pricing research, since it implies that non-continuous trading, bid-ask spreads, and other market imperfections substantially influence option prices. This implication is important, both because incorporating these types of market imperfections into option pricing models is much more difficult than, for example, altering the dynamics of the underlying asset and also because it suggests that researchers cannot learn about option investor expectations by filtering option

Considerable research effort has focused on the forecasting of asset return volatility. Debate in this area centers around the performance of time series models, in particular GARCH, relative to implied volatility from observed option premiums. Existing literature suggests that the performance of any volatility forecast is sensitive to both the data and forecast horizon of interest. This paper rigorously examines the performance of several alternative volatility forecasts for fed cattle, feeder cattle, and corn cash price returns. Forecasts include time series, implied volatility, and composite specifications. The results provide considerable insight into the performance of these alternative volatility forecasting procedures over a range of relevant forecast horizons. The evidence suggests that composite methods be used when both time series and implied volatilities are available. Insight is also gained into the performance of procedures used for scaling one-period volatility forecasts to longer horizons. However, consistent with the existing volatility forecasting literature, this research confirms the difficulty in finding a “best ” volatility forecasting method across alternative data sets and horizons.

The unbiasedness tests of implied volatility as a forecast of future realized volatility have found implied volatility to be a biased predictor. We explain this puzzle by recognizing that option prices contain a market risk premium not only on the asset itself, but also on its volatility. We show using a stochastic volatility model, that a call option price can be represented as an expected value of the Black-Scholes formula evaluated at the average integrated volatility. If we allow volatility risk to be priced, this expectation should be taken under the risk-neutral probability measure, and can be decomposed into the expectation with respect to the physical measure and the risk-premium term. This term is just a linear function of the unobservable spot volatility. The decomposition explains the bias documented in the empirical literature and shows that the realized and historical volatility, which are used in the tests, are in fact the estimates of the unobserved quadratic variation and spot volatility of the stock-return generating process. Therefore, the use of these estimates generates the error-in-the-variables problem. We provide an empirical example based on the S&P 100 returns and the VIX index. We find, that when we take into an account the risk-premium and use efficient methods to estimate volatility, the unbiasedness hypothesis can not be rejected, and the point estimate of the slope in the traditional regression is exactly equal to 1.

An investigation into the causes and consequences of asymmetric volatility

Abstract. We propose an adaptive algorithm for tracking of historical volatility. The algorithm is built under the assumption that the historical volatility function belongs to the Stone-Ibragimov-Khasminskii class of k times differentiable functions with bounded highest derivative and its subclass of functions satisfying a differential inequalities. We construct an estimator of the Kalman filter type and show optimality of the estimator’s convergence rate to zero as sample size n → ∞. This estimator is in the framework of GARCH design, but a tuning procedure of its parameters is faster than with traditional GARCH techniques.