Memory in returns and volatilities of futures' contracts

Various authors claim to have found evidence of stochastic long‐memory behavior in futures’ contract returns using the Hurst statistic. This paper reexamines futures’ returns for evidence of persistent behavior using a biased‐corrected version of the Hurst statistic, a nonparametric spectral test, and a spectral‐regression estimate of the long‐memory parameter. Results based on these new methods provide no evidence for persistent behavior in futures’ returns. However, they provide overwhelming evidence of long‐memory behavior for the volatility of futures’ returns. This finding adds to the emerging literature on persistent volatility in financial markets and suggests the use of new methods of forecasting volatility, assessing risk, and optimizing portfolios in futures’ markets. © 2000 John Wiley & Sons, Inc. Jrl Fut Mark 20:525–543, 2000     

Realized volatility and correlation in energy futures markets

Using high‐frequency returns, realized volatility and correlation of the NYMEX light, sweet crude oil, and Henry‐Hub natural gas futures contracts are examined. The unconditional distributions of daily returns and daily realized variances are non‐Gaussian, whereas the distributions of the standardized returns (normalized by the realized standard deviation) and the (logarithms of) realized standard deviations appear approximately Gaussian. The (logarithms of) standard deviations exhibit long‐memory, but the realized correlation between the two futures does not, implying rather weak inter‐market linkage in the long run. There is evidence of asymmetric volatility for natural gas but not for crude oil futures. Finally, realized crude oil futures volatility responds with an increase in the weeks immediately before the OPEC events recommending price increases. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:993–1011, 2008     

Speculation and volatility—A time-varying approach applied on Chinese commodity futures markets

Experts have long discussed and empirically investigated whether speculative activity increases volatility on commodity futures markets. Little empirical research, however, analyzes the role of speculators on commodity futures markets in China. Using time-varying vector autoregression models with stochastic volatility, this paper investigates for four heavily traded metal and agricultural contracts, how the relationship between returns volatility and speculation evolves over time. Our findings indicate that speculative activity has little to no impact on volatility. On the contrary, for all commodities examined, returns volatility seems to amplify speculation.     

Long memory in commodity futures volatility: A wavelet perspective

The authors reexamine the volatility of agricultural commodity futures for evidence of fractional integration, providing new empirical results and extending the extant literature in important dimensions. First, they utilize two relatively new estimators based on wavelets, which are generally superior to, for example, the popular estimator by J. Geweke and S. Porter‐Hudak (GPH; 1983) and exact maximum likelihood estimators (MLEs) on the basis of mean squared error (MSE). Second, they provide simulations to contrast their point estimates with those obtained by a fractionally integrated GARCH (generalized autoregressive conditional heteroscedasticity) model. Third, they conduct a wavelet coef.cient decomposition of futures volatility. They .nd that futures volatilities display the self‐similarity property consistent with long memory and that futures volatilities exhibit persistent long memory with .nite unconditional variance. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:411–437, 2007     

Economic uncertainty,trading activity,and commodity futures volatility

This paper investigates the dynamics of commodity futures volatility. I derive the variance decomposition for the futures basis and show unexpected excess returns result from new information about expected future interest rates, convenience yields, and risk premia. Measures of uncertainty in economic conditions have significant predictive power for realized volatility of commodity futures returns, after controlling for lagged volatility, returns, commodity index trading, hedging pressure, and other trading activity, even during the so-called “index financialization” period. During this period, hedge fund performance predicts volatility in grain commodities, which are affected by the US ethanol mandate.     

Return dynamics during periods of high speculation in a thinly traded commodity market

This article studies the effects of speculation in a thinly traded commodity futures market, paying particular attention to periods characterized by high-speculative activity of long–short speculators. Using the speculation ratio as a daily measure for long–short speculation, we employ generalized autoregressive conditional heteroscedasticity regressions to study its impact on return dynamics. Our results for the Chicago Mercantile Exchange feeder cattle futures market suggest that futures returns are predominantly explained by fundamentals, but their volatility is significantly driven by the speculation ratio. This relationship holds for periods of high- and low-speculative activity alike.     

The realized volatility of FTSE‐100 futures prices

Five‐minute returns from FTSE‐100 index futures contracts are used to obtain accurate estimates of daily index volatility from January 1986 to December 1998. These realized volatility measures are used to obtain inferences about the distributional and autocorrelation properties of FTSE‐100 volatility. The distribution of volatility measured daily is similar to lognormal while the volatility time series has persistent positive autocorrelation that displays long‐memory effects. The distribution of daily returns standardized using the measures of realized volatility is shown to be close to normal, unlike the unconditional distribution. © 2002 Wiley Periodicals, Inc. Jrl Fut Mark 22:627–648, 2002     

Modeling discontinuous periodic conditional volatility: Evidence from the commodity futures market

This paper examines a wide variety of models that allow for complex and discontinuous periodic variation in conditional volatility. The value of these models (including augmented versions of existing models) is demonstrated with an application to high frequency commodity futures return data. Their use is necessary, in this context, because commodity futures returns exhibit discontinuous intraday and interday periodicities in conditional volatility. The former of these effects is well documented for various asset returns; however, the latter is unique amongst commodity futures returns, where contract delivery and climate are driving forces. Using six years of high‐frequency cocoa futures data, the results show that these characteristics of conditional return volatility are most adequately captured by a spline‐version of the periodic generalized autoregressive conditional heteroscedastic (PGARCH) model. This model also provides superior forecasts of future return volatility that are robust to variation in the loss function assumed by the user, and are shown to be beneficial to users of Value‐at‐Risk (VaR) models. © 2004 Wiley Periodicals, Inc. Jrl Fut Mark 24:805–834, 2004     

Jumping hedges: An examination of movements in copper spot and futures markets

Price risk is an important factor for both copper purchasers, who use the commodity as a major input in their production process, and copper refiners, who must deal with cash‐flow volatility. Information from NYMEX cash and futures prices is used to examine optimal hedging behavior for agents in copper markets. A bivariate GARCH‐jump model with autoregressive jump intensity is proposed to capture the features of the joint distribution of cash and futures returns over two subperiods with different dominant pricing regimes. It is found that during the earlier producerpricing regime this specification is not needed, whereas for the later exchange pricing era jump dynamics stemming from a common jump across cash and futures series are significant in explaining the dynamics in both daily and weekly data sets. Results from the model are used to under‐take both within‐sample and out‐of‐sample hedging exercises. These results indicate that there are important gains to be made from a time‐varying optimal hedging strategy that incorporates the information from the common jump dynamics. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:169–188, 2006     

Managed futures,positive feedback trading,and futures price volatility

A major issue in recent years is the role that large, managed futures funds and pools play in futures markets. Many market participants argue that managed futures trading increases price volatility due to the size of managed futures trading and reliance on positive feedback trading systems. The purpose of this study is to provide new evidence on the impact of managed futures trading on futures price volatility. A unique data set on managed futures trading is analyzed for the period 1 December 1988 through 31 March 1989. The data set includes the daily trading volume of large commodity pools for 36 different futures markets. Regression results are unequivocal with respect to the impact of commodity pool trading on futures price volatility. For the 72 estimated regressions (two for each market), the coefficient on commodity pool trading volume is significantly different from zero in only four cases. These results constitute strong evidence that, at least for this sample period, commodity pool trading is not associated with increases in futures price volatility. © 1999 John Wiley & Sons, Inc. Jrl Fut Mark 19: 759–776, 1999     

国际股票市场收益率和波动率的长记忆性研究

股票市场长记忆性问题是金融学研究的一个热点问题,对于市场有效性的研究和系统非线性结构的分析有着重要的意义。本文运用修正R/S分析和V/S分析两种方法对世界上28个国家(地区)的股票指数的日、周收益序列和日、周收益波动序列进行了完整的长记忆性研究。结果表明:对于收益序列,以美国为代表的大多数发达国家股市一般不存在长记忆性,而中国等发展中国家大多存在显著的长记忆性,尤其中国股市的长记忆性最强;对于收益波动序列,所有国家(地区)都具有长记忆性,并强于收益序列。     

What moves German Bund futures contracts on the Eurex?

The German 10‐year Bund futures contract traded on the Eurex futures and options exchange in Frankfurt became the world's most actively traded derivative product by the end of 1999. In this article, we provide a detailed exploration of the interday and intraday return volatility in the Bund futures contract using a sample of five‐min returns from 1997 to 1998. The evolution of interday volatility is described best by a MA(1)‐fractionally integrated process that allows for the long‐memory features. At the intraday level, we find that macroeconomic announcements from both Germany and the U.S. are an important source of volatility. Among the various German announcements, we identify the IFO industry survey of business climate, industrial production (preliminary), and Bundesbank policy meeting as being by far the most important. The three most significant U.S. announcements include the employment report, the National Association of Purchasing Managers (NAPM) survey, and employment costs. Overall, U.S. macroeconomic announcements have a far greater impact on the Bund futures market than their German counterparts. © 2002 Wiley Periodicals, Inc. Jrl Fut Mark 22:679–696, 2002     

Testing mean reversion in financial market volatility: Evidence from S&P 500 index futures

This article presents a comprehensive study of continuous time GARCH (generalized autoregressive conditional heteroskedastic) modeling with the thintailed normal and the fat‐tailed Student's‐t and generalized error distributions (GED). The study measures the degree of mean reversion in financial market volatility based on the relationship between discrete‐time GARCH and continuoustime diffusion models. The convergence results based on the aforementioned distribution functions are shown to have similar implications for testing mean reversion in stochastic volatility. Alternative models are compared in terms of their ability to capture mean‐reverting behavior of futures market volatility. The empirical evidence obtained from the S&P 500 index futures indicates that the conditional variance, log‐variance, and standard deviation of futures returns are pulled back to some long‐run average level over time. The study also compares the performance of alternative GARCH models with normal, Student's‐ t, and GED density in terms of their power to predict one‐day‐ahead realized volatility of index futures returns and provides some implications for pricing futures options. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:1–33, 2008     

Valuing real options using implied binomial trees and commodity futures options

A real option on a commodity is valued using an implied binomial tree (IBT) calibrated using commodity futures options prices. Estimating an IBT in the absence of spot options (the norm for commodities) allows real option models to be calibrated for the first time to market‐implied probability distributions for commodity prices. In addition, the existence of long‐dated futures options means that good volatility estimates may now be incorporated into capital budgeting evaluations of real options projects with long planning horizons. An example is given using gold futures options and a real option to extract gold from a mine. A detailed out‐of‐sample test is included that shows how IBT option pricing errors evolve on subtrees emanating from future levels of the underlying asset. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:203–226, 2007     

A No‐Arbitrage Fractional Cointegration Model for Futures and Spot Daily Ranges

The no‐arbitrage relation between futures and spot prices implies an analogous relation between futures and spot daily ranges. The long‐memory features of the range‐based volatility estimators are analyzed, and fractional cointegration is tested in a semi‐parametric framework. In particular, the no‐arbitrage condition is used to derive a long‐run relationship between volatility measures and to justify the use of a fractional vector error correction model (FVECM) to study their dynamic relationship. The out‐of‐sample forecasting superiority of FVECM, with respect to alternative models, is documented. The results highlight the importance of incorporating the long‐run equilibrium in volatilities to obtain better forecasts, given the information content in the volatility of futures prices. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark 33:77–102, 2013     

Volatility of volatility is (also) rough

Using high-frequency data for major volatility indexes, we compute the volatility of volatility and show that its logarithm follows a fractional Brownian motion with Hurst parameter smaller than 1/2 thereby extending to the volatility asset class the recent findings obtained for the equity index markets. The results confirm that the volatility of volatility is a rough process and it possesses the long memory property. We also show that the correlation between the volatility and the volatility of volatility is positive, consistent with observations in the volatility option market. Lastly, a robustness check using volatility futures confirms the findings.     

Dual long memory property in returns and volatility: Evidence from the CEE countries' stock markets

This paper investigates the presence of long memory in the eight Central and Eastern European (CEE) countries' stock market, using the ARFIMA, GPH, FIGARCH and HYGARCH models. The data set consists of daily returns, and long memory tests are carried out both for the returns and volatilities of these series. The results of the ARFIMA and GPH models indicate the existence of long memory in five of eight return series. The results also suggest that long memory dynamics in the returns and volatility might be modeled by using the ARFIMA–FIGARCH and ARFIMA–HYGARCH models. The results of these models indicate strong evidence of long memory both in conditional mean and conditional variance. Moreover, the ARFIMA–FIGARCH model provides the better out-of-sample forecast for the sampled stock markets.     

The stock closing calland futures price behavior: Evidence from the Taiwan futures market

This study examines the behavior of futures prices around stock market close before and after changes to the batching period of the stock closing call. On July 1, 2002, the Taiwan Stock Exchange expanded the length of the batching period roughly 10‐fold, from an average of 30 seconds to 5 minutes. This change presents an opportunity to analyze how a stock closing method affects the behavior of index futures prices. Empirical results indicate that an increase in the length of the batching period affects the return volatility and trading volume of index futures contracts around stock market close. Furthermore, preclose stock returns have a great impact on extended futures returns when the batching period of the stock closing call is long. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:1003–1019, 2007     

Samuelson hypothesis,arbitrage activity,and futures term premiums

The Samuelson hypothesis asserts that futures volatility increases as maturity decreases. On the basis of 10 US commodity futures and by capturing the dynamics of the futures volatility terms structure with three factors, we show that in most markets the slope factor is strongly negative in certain periods and at best only weakly negative in other periods. High inventory levels are found to correspond to flatter volatility term structures in seven futures. This finding is consistent with the linkage between carry arbitrage and the Samuelson hypothesis. We also find that a flatter volatility term structure corresponds to lower absolute futures term premiums.     

Minimum capital requirement calculations for UK futures

Key to the imposition of appropriate minimum capital requirements on a daily basis is accurate volatility estimation. Here, measures are presented based on discrete estimation of aggregated high‐frequency UK futures realizations underpinned by a continuous time framework. Squared and absolute returns are incorporated into the measurement process so as to rely on the quadratic variation of a diffusion process and be robust in the presence of fat tails. The realized volatility estimates incorporate the long memory property. The dynamics of the volatility variable are adequately captured. Resulting rescaled returns are applied to minimum capital requirement calculations. © 2004 Wiley Periodicals, Inc. Jrl Fut Mark 24:193–220, 2004