Volatility term structures in commodity markets

In this study, we comprehensively examine the volatility term structures in commodity markets. We model state-dependent spillovers in principal components (PCs) of the volatility term structures of different commodities, as well as that of the equity market. We detect strong economic links and a substantial interconnectedness of the volatility term structures of commodities. Accounting for intra-commodity-market spillovers significantly improves out-of-sample forecasts of the components of the volatility term structure. Spillovers following macroeconomic news announcements account for a large proportion of this forecast power. There thus seems to be substantial information transmission between different commodity markets.     

Forecast errors before and during the Great Moderation

This paper investigates the change in private sector and Federal Reserve forecasts before and during the Great Moderation. We view the Great Moderation as a natural experiment. Using forecasts produced by the Survey of Professional Forecasters and the Federal Reserve (Greenbook forecasts) we investigate three questions: (1) How large was the decline in forecast errors? (2) Did forecast accuracy improve relative to the decline in volatility of growth and inflation? (3) Did forecasters respond to the Great Moderation? We find that the absolute median error as well as the cross-sectional volatility of forecast errors decreased significantly. Forecasters appeared to have narrowed the dispersion of their forecasts in response to the Great Moderation. Forecast accuracy did not improve relative to the reduction in the volatility of the economy.     

Information content of volatility spreads

This study reexamines the determinants of volatility spreads and suggests a new forecast of future volatilities. Contrary to earlier volatility forecasts, the newly introduced forecast is applicable when investors are not risk‐neutral or when underlying returns do not follow a Gaussian probability distribution. This implies that the method is consistent with the presence of risk premia for other risks such as volatility risk. Using S&P 500 index options, we show that the new volatility forecast outperforms other volatility forecasts including risk‐neutral implied volatility and historical volatility in two aspects. First, the new forecast is superior to other estimates in terms of forecasting errors for future realized volatilities. Second, it is an unbiased estimator of future realized volatilities. This is shown using an encompassing regression analysis. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:533–558, 2010     

Forecasting bitcoin volatility: Evidence from the options market

This paper studies a large number of bitcoin (BTC) options traded on the options exchange Deribit. We use the trades to calculate implied volatility (IV) and analyze if volatility forecasts can be improved using such information. IV is less accurate than AutoRegressive–Moving-Average or Heterogeneous Auto-Regressive model forecasts in predicting short-term BTC volatility (1 day ahead), but superior in predicting long-term volatility (7, 10, 15 days ahead). Furthermore, a combination of IV and model-based forecasts provides the highest accuracy for all forecasting horizons revealing that the BTC options market contains unique information.     

The bias in time series volatility forecasts

By Jensen's inequality, a model's forecasts of the variance and standard deviation of returns cannot both be unbiased. This study explores the bias in GARCH type model forecasts of the standard deviation of returns, which we argue is the more appropriate volatility measure for most financial applications. For a wide variety of markets, the GARCH, EGARCH, and GJR (or TGARCH) models tend to persistently over‐estimate the standard deviation of returns, whereas the ARLS model of L. Ederington and W. Guan (2005a) does not. Furthermore, the GARCH and GJR forecasts are especially biased following high volatility days, which cause a large jump in forecast volatility, which is rarely fully realized. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:305–323, 2010     

Properties and the predictive power of implied volatility in the New Zealand dairy market

This study develops a dairy implied volatility index (DVIX), derived from New Zealand Exchange traded options on whole milk powder (WMP) futures. We document an inverse return–volatility relation which is asymmetric, where increases in WMP futures prices are associated with larger absolute changes in the DVIX than decreases. In sample, the results strongly suggest that the DVIX has a high information content regarding conditional variance and that the inclusion of historical information further improves the predictive power. Out of sample, we find that the DVIX provides substantial information about future realized volatility. We also document that a combination of historical volatility and the DVIX provides the best out-of-sample forecasts.     

Measuring and forecasting S&P 500 index‐futures volatility using high‐frequency data

In the 24‐hr foreign exchange market, Andersen and Bollerslev measure and forecast volatility using intraday returns rather than daily returns. Trading in equity markets only occurs during part of the day, and volatility during nontrading hours may differ from the volatility during trading hours. This paper compares various measures and forecasts of volatility in equity markets. In the absence of overnight trading it is shown that the daily volatility is best measured by the sum of intraday squared 5‐min returns, excluding the overnight return. In the absence of overnight trading, the best daily forecast of volatility is produced by modeling overnight volatility differently from intraday volatility. © 2002 Wiley Periodicals, Inc. Jrl Fut Mark 22:497–518, 2002     

中国股市波动的CARR模型分析

ARCH/GARCH模型在波动性的预测已被学者广泛使用并在实证上得到良好的效果。本文以上海股市为研究对象,分别运用CARR模型和GARCH模型进行波动性预测,进而对两种方法的预测能力进行比较,实证结果表明CARR模型在拟合波动性方面优于GARCH模型。     

The quality of volatility traded on the over‐the‐counter currency market: A multiple horizons study

Previous studies of the quality of market‐forecasted volatility have used the volatility that is implied by exchange‐traded option prices. The use of implied volatility in estimating the market view of future volatility has suffered from variable measurement errors, such as the non‐synchronization of option and underlying asset prices, the expiration‐day effect, and the volatility smile effect. This study circumvents these problems by using the quoted implied volatility from the over‐the‐counter (OTC) currency option market, in which traders quote prices in terms of volatility. Furthermore, the OTC currency options have daily quotes for standard maturities, which allows the study to look at the market's ability to forecast future volatility for different horizons. The study finds that quoted implied volatility subsumes the information content of historically based forecasts at shorter horizons, and the former is as good as the latter at longer horizons. These results are consistent with the argument that measurement errors have a substantial effect on the implied volatility estimator and the quality of the inferences that are based on it. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:261–285, 2003     

Measuring implied volatility: Is an average better? Which average?

Options researchers have argued that by averaging together implied standard deviations, or ISDs, calculated from several options with the same expiry but different strikes, the noise in individual ISDs can be reduced, yielding a better measure of the market's volatility expectation. Various options researchers have suggested different weighting schemes for calculating these averages. In the forecasting literature, econometricians have made the same argument but suggested quite different weighting schemes. Ignoring both literatures, commercial vendors calculate ISD averages using their own weightings. We compare the averages proposed in both the options and econometrics literatures and the averages used by major commercial vendors for the S&P 500 futures options market. Although some averages forecast better than others, we find that the question of the best weighting scheme is of secondary importance. More important is the fact that the ISDs are upward biased measures of expected volatility. Fortunately, this bias is stable over time, so past bias patterns can be used to obtain unbiased volatility forecasts. Once this is done, most ISD averages forecast better than time series and naive models, and the differences between the averages produced by the various proposed weighting schemes are small. © 2002 Wiley Publications, Inc. Jrl Fut Mark 22:811–837, 2002     

基于高频数据的波动率与成交量动态关系研究

传统的价量分析都是从低频数据来分析股票市场上波动率、收益率与成交量之间的关系。基于高频数据,利用分位数回归并结合高频数据的波动率估计方法对高频数据中所呈现出的价量关系进行研究,并分析了股票价格跳跃过程所带来的跳跃方差与成交量之间的关系。实证分析表明：指数及个股收益率与成交量之间的关系并不显著;波动率、跳跃与成交量之间存在着显著相关的关系,个股的波动率与成交量之间的关系显著并呈现出正向相关关系,而指数的波动率与成交量之间呈现出一种负向关系,并且关系比较微弱;个股的成交量的改变会导致股票价格的跳跃方差的减小,而指数的成交量的改变则使得指数的跳跃方差增大。     

Uncertainty and the volatility forecasting power of option-implied volatility

This study investigates the impact of uncertainty on the volatility forecasting power of option-implied volatility. Option-implied volatility is a powerful predictor of future volatility, particularly during periods of high uncertainty. This is consistent with option-implied volatility being largely determined by volatility-informed traders (rather than directional traders) when uncertainty is high. New volatility forecasting models that incorporate such interaction outperform benchmark models, both in- and out-of-sample. The new models also better predict future volatility during the 2008 global financial crisis, for which benchmark models perform poorly. The results are robust to alternative choices of benchmark models, loss functions, and estimation windows.     

汇改对我国中小企业出口的影响测度与预测——基于汇改后月度数据的实证分析

当前我国中小企业出口经营困境凸显,进一步汇改是否会加剧其困境成为关注的焦点。本文基于汇改后的月度数据,采用GARCH模型分析各次汇改对汇率弹性的影响特征,构建向量误差修正模型测度和预测汇改对中小企业出口的影响。结果表明:汇改促使人民币每升值1%,其出口减少3.874%;汇率弹性增强1%,其出口减少0.034%。预测的中小企业出口总额较为平稳。进一步汇改以增强汇率弹性为核心不会对中小企业出口总量造成大的冲击。     

Multivariate realized volatility forecasts of agricultural commodity futures

We forecast the multivariate realized volatility of agricultural commodity futures by constructing multivariate heterogeneous autoregressive (MHAR) models with flexible heteroscedastic error structures that allow for non-Gaussian distribution, stochastic volatility, and heteroscedastic and serial dependence. We evaluate the forecast performances of various models based on both statistical and economic criteria. The in-sample and out-of-sample results suggest that the proposed MHAR models allowing for flexible heteroscedastic covariance structures outperform the benchmark MHAR models. In addition, the proposed Bayesian MHAR models allowing for t innovations improve both in-sample and out-of-sample forecast performance of the corresponding MHAR models with Gaussian innovations.     

The forecast quality of CBOE implied volatility indexes

We examine the forecast quality of Chicago Board Options Exchange (CBOE) implied volatility indexes based on the Nasdaq 100 and Standard and Poor's 100 and 500 stock indexes. We find that the forecast quality of CBOE implied volatilities for the S&P 100 (VXO) and S&P 500 (VIX) has improved since 1995. Implied volatilities for the Nasdaq 100 (VXN) appear to provide even higher quality forecasts of future volatility. We further find that attenuation biases induced by the econometric problem of errors in variables appear to have largely disappeared from CBOE volatility index data since 1995. © 2005 Wiley Periodicals, Inc. Jrl Fut Mark 25:339–373, 2005     

Forecasting volatility: Roles of sampling frequency and forecasting horizon

This study empirically tests how and to what extent the choice of the sampling frequency, the realized volatility (RV) measure, the forecasting horizon and the time‐series model affect the quality of volatility forecasting. Using highly synchronous executable quotes retrieved from an electronic trading platform, the study avoids the influence of various market microstructure factors in measuring RV with high‐frequency intraday data and in inferring implied volatility (IV) from option prices. The study shows that excluding non‐trading‐time volatility produces significant downward bias of RV by as much as 36%. Quality of prediction is significantly affected by the forecasting horizon and RV model, but is largely immune from the choice of sampling frequency. Consistent with prior research, IV outperforms time‐series forecasts; however, the information content of historical volatility critically depends on the choice of RV measure. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark     

VIX futures and its closed‐form pricing through an affine GARCH model with realized variance

This paper studies the forecasting of volatility index (VIX) and the pricing of its futures by a generalized affine realized volatility model proposed by Christoffersen et al. This model is a weighted average of a GARCH and a pure realized variance (RV) model that incorporates each volatility component into the new dynamics. We rewrite the VIX in terms of both volatility components and then derive closed‐form formulas for the VIX forecasting and its futures pricing. Our empirical studies find that a unification of the GARCH and the RV in the modeling substantially improves the forecasting of this index and the pricing of its futures.     

Robustness and exchange rate volatility

This paper studies exchange rate volatility within the context of the monetary model of exchange rates. We assume that agents regard this model as merely a benchmark, or reference model, and attempt to construct forecasts that are robust to model misspecification. We show that revisions of robust forecasts are more volatile than revisions of nonrobust forecasts, and that empirically plausible concerns for model misspecification can explain observed exchange rate volatility. We also briefly discuss the implications of robust forecasts for a number of other exchange rate puzzles.     

AN examination of short QQQ option trades

This study shows that unconditional QQQ option selling strategies from January 2001 through November 2004 are generally significantly profitable after transactions costs. However, when straddle and strangle sales are combined with purchases of out of the money puts, few of the strategies are significantly profitable. Profits improve when the QQQ Volatility Index is high relative to time series volatility forecasts, but only when actual volatility is forecast to be moderate. Active delta‐hedging reduces profitability, whereas stop loss/take profit orders enhance profitability. Overall, QQQ short volatility trades appear to be less compelling than what others have found with S&P options. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:739–770, 2007     

Realized Volatility Forecast: Structural Breaks,Long Memory,Asymmetry, and Day‐of‐the‐Week Effect

We investigate the properties of the realized volatility in Chinese stock markets by employing the high‐frequency data of Shanghai Stock Exchange Composite Index and four individual stocks from Shanghai Stock Exchange and Shenzhen Stock Exchange, and find that the volatility exhibits the properties of long‐term memory, structural breaks, asymmetry, and day‐of‐the‐week effect. In addition, the structural breaks only partially explain the long memory. To capture these properties simultaneously, we derive an adaptive asymmetry heterogeneous autoregressive model with day‐of‐the‐week effect and fractionally integrated generalized autoregressive conditional heteroskedasticity errors (HAR‐D‐FIGARCH) and use it to conduct a forecast of realized volatility. Compared with other heterogeneous autoregressive realized volatility models, the proposed model improves the in‐sample fit significantly. The proposed model is the best model for the day‐ahead realized volatility forecasts among the six models based on various loss functions by utilizing the superior predictive ability test.