قدرت پیش بینی نوسانات ضمنی : شواهدی از 35 بازار آتی

Using data from 35 futures options markets from eight separate exchanges, we test how well the implied volatilities (IVs) embedded in option prices predict subsequently realized volatility (RV) in the underlying futures. We find that for this broad array of futures options, IV performs well in a relative sense. For a large majority of the commodities studied, the implieds outperform historical volatility (HV) as a predictor of the subsequently RV in the underlying futures prices over the remaining life of the option. Indeed, in most markets examined, regardless of whether it is modeled as a simple moving average or in a GARCH framework, HV contains no economically significant predictive information beyond what is already incorporated in IV. These findings add to previous research that has focused on currency and crude oil futures by extending the analysis into a very broad array of contracts and exchanges. Our results are consistent with the hypothesis that futures options markets in general, with their minimal trading frictions, are efficient.

How well does implied volatility (IV) predict future realized volatility (RV)? Research so far has failed to provide a definitive answer as results on this empirical question have been mixed. The purpose of this study is to re-examine the predictive power of IVs, relative to historical and GARCH-based volatility estimates. We accomplish this using a battery of tests with extensive data on 35 futures options covering a wide variety of asset classes and exchanges. Solving an option pricing model backwards using an observed option price provides an estimate of the IV of returns on the underlying asset. The expected value of future RV should be equal to IV if (1) options are priced correctly and (2) the option pricing formula is correct. We find some support for this joint-hypothesis: Implieds are biased yet better predictors of RV than alternative historical volatility (HV) estimates. Early research on the predictive content of IV found that IV explains variation in future volatilities better than HV. Latané and Rendleman (1976), Chiras and Manaster (1978), Schmalensee and Trippi (1978), and Beckers (1981) utilized stock options and the basic Black and Scholes (1973) option pricing model without considering dividends, the possibility of early exercise, different closing times in stock and option markets, and the various options’ terms to maturity, to arrive at this conclusion. In subsequent research, Kumar and Shastri (1990), Randolph et al. (1990), Day and Lewis (1992), Lamoureux and Lastrapes (1993), and Canina and Figlewski (1993), all of which examine either options on individual stocks or options on the cash S&P 100 index, use more sophisticated methodologies with more careful treatment of the data. They generally find that IV is a poor forecast of the subsequently RV over the remaining life of the option. For example, Canina and Figlewski (1993) use a regression approach to examine the predictive content of S&P 100 index options and find virtually no relation between the implied and subsequently RV over the remaining life of the option, despite the fact that the HVs and future RVs are related. Some of these studies also find that IV has little power to predict short-run changes in the volatility of the underlying asset, e.g. over a one-week horizon, compared to predictions that could be derived from time-series models. Specifically, Day and Lewis (1992) and Lamoureux and Lastrapes (1993) analyze the predictive power of IV within the context of GARCH-type models. They find that IV has some predictive power, but that GARCH and/or HV improve this predictive power. In contrast to this later stream of research, Christensen and Prabhala (1988), using a monthly sampling frequency with non-overlapping data, find that IV is a good predictor for RV. Their results also demonstrate that the predictive ability of IV improved after the structural pricing shift in the OEX market that followed the 1987 stock market crash. Given the equivocal results and conclusions in stock market options alone, it is clear that further research on the predictive power of IV is warranted. Only two studies of which we are aware have examined the performance of IV as a predictor outside of equity markets (Day and Lewis, 1993; Jorion, 1995). Both studies find that the IVs embedded in crude oil and foreign currency futures options, respectively, do provide a reasonably good forecast of the ultimately RVs in the underlying futures; for example, both studies find that the information content of the implieds for predicting volatility in the underlying asset over short time horizons is superior to the information content of GARCH models conditioned on HV. Jorion (1995) also demonstrates, using the Canina and Figlewski (1993) regression approach, that while IVs are not completely unbiased estimates of RVs, in currency futures the implieds outperform HV as a predictor of RV over the remaining life of the option. 4 Our study is motivated by two major shortcomings in the previous literature. First, as noted above, most previous work has focused on options on individual stocks or on cash market stock indices. These options do not trade on the same exchange as their underlying asset, and the exchanges do not have the same daily closing time. The closing prices used by these studies would not be synchronous. Worse, as Fleming et al. (1996) show, trading costs in cash stock markets are relatively high, rendering arbitrage transactions involving both options and their underlying stocks more difficult. Thus, one major contribution of our study is that we use data from futures markets, where the options on futures and the underlying futures contracts trade on the same floor. These markets have trading costs that are orders of magnitude lower than those involving cash market transactions. Lower trading costs increase the feasibility of arbitrage, making the assumption of unlimited arbitrage inherent to option pricing models more tenable. Furthermore, while the stock market closes fifteen minutes prior to the closing of the options market (Harvey and Whaley, 1992) the futures and options markets we analyze close simultaneously. Studies based on stock options may not obtain consistent estimates of IV because the option prices, underlying security price, and information about the underlying asset are not observed simultaneously. This would introduce measurement error as simultaneous option and underlying asset prices are required to estimate IV.5 Another shortcoming of the previous literature, which again arises from the predominant focus on equity markets, is incompleteness in terms of the types of assets examined. One possible reason why Day and Lewis (1993) and Jorion (1995) obtain very different results than most studies that examine equity markets is that that they use futures options, in which trading frictions and measurement errors are much lower. However, an equally plausible explanation is that the time series properties of various asset classes differ, and IV may be a better predictor for some assets and options (e.g., foreign exchange, crude oil) than for others (equity markets).6 Thus, the most important contribution of our study is that we examine futures options for a wide variety of asset classes, specifically, 35 different markets traded on eight different exchanges. In addition to futures options on an equity index (the S&P 500), currencies and crude oil, we also examine those on short-term and long-term interest rates, agricultural commodities, livestock, metals, refined petroleum products, and natural gas. By examining the predictive content of IV over such a wide range of futures options and markets, and by seeing if the predictive content varies across different categories of asset classes trading on different exchanges, we hope to determine whether Jorion’s (1995) conjecture that IV is likely to be a good predictor for futures options in general is correct, or alternatively, if Jorion’s results are specific to currency futures options only. The balance of the paper is organized as follows: We describe our data and discuss related issues in Section 2. We present models, develop hypotheses, and present results for regression tests of implied and HV as predictors of RV in Section 3. Section 4 presents tests of the predictive power of IV vis-à-vis forecasts provided by a frequently-used GARCH model. Section 5 concludes the paper.

Using data from 35 options on futures, we test how well the IVs embedded in options prices predict subsequently RV in the underlying futures. Our tests analyze the unbiasedness of IV as a predictor, as well as the usefulness of IV relative to other alternatives (such as HV or forecasts from a GARCH model) that are commonly employed to predict future volatility. Our study is an improvement over prior research because we examine markets in which the options and their underlying futures trade simultaneously with relatively low transactions costs and minimal trading frictions, and because we survey a much broader variety of underlying asset classes (e.g. stocks, bonds, money market securities, currencies, agricultural commodities, industrial commodities, metals, etc.) than in previous studies. We find that for this broad array of futures options, IV, though not a completely unbiased predictor of future volatility, performs well in a relative sense. For an overwhelming majority of the 35 commodities studied, IV outperformed HV as a predictor of the subsequently RV in the underlying futures prices over the remaining life of the option. Furthermore, in most markets, HV does not appear to contain any information that is not already incorporated in the IV. These results appear to be robust across differing terms to maturity, and for S&P 500 options, across sample periods as well. When we replace simple 30 day moving average HVs with recursive forecasts from GARCH models, we find little difference in predictive power. Our findings are qualitatively similar to those in Christensen and Prabhala (1988) for equity indices and are consistent with the weak-form efficiency of futures options markets, in that the volatility information embedded in current option prices is a better predictor of future volatility than historical measures of volatility, regardless of how the latter are modeled. In all of the markets we examine, the futures and options contracts trade on the same exchange, their closing prices are less likely to be subject to non-synchronous trading problems, and transactions costs are relatively low. IV, while not a completely unbiased forecast of the RV, appears to dominate HV in virtually all of these markets. Despite considerable effort, we have been unable to discern any obvious pattern in our results, either by exchange, type of commodity, sample period, or remaining term to maturity. Thus, our findings confirm and extend Jorion
s (1995) results for currency futures options. They indicate that futures options markets in general, and by extension, markets in which trading frictions are minimal, do tend to be relatively efficient.