A comparative study of alternative extreme‐value volatility estimators

Recent advances in econometric methodology and newly available sources of data are used to examine empirically the performance of the various extreme‐value volatility estimators that have been proposed over the past two decades. Overwhelming support is found for the use of extreme‐value estimators when computing daily volatility measures across all assets: Daily extreme‐value volatility estimators are both less biased and substantially more efficient than the traditional close‐to‐close estimator. In the case of weekly and monthly measures, the results still suggest that extreme‐value estimators are appropriate, but the evidence is more mixed. © 2005 Wiley Periodicals, Inc. Jrl Fut Mark 25:873–892, 2005     

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     

The Information Content of Model‐Free Implied Volatility

This study examines the information content of model‐free implied volatility (MFIV) estimates with respect to the options and futures markets in Hong Kong. In this study, the volatility forecasting performance of MFIV is compared, using different prediction horizons, to IV estimates based on Black's futures option pricing model (BIV) and time‐series forecasts based on historical volatility (TS‐HV). The results show that the BIV prediction is unbiased for different horizon forecasts. MFIV outperforms TS‐HV forecasts and, most importantly, BIV subsumes the information content of both MFIV and TS‐HV forecasts. The results are largely maintained for next‐day forecasts but the forecasting quality of the two IV measures declines as expiration day approaches. The information contents of MFIV and TS‐HV forecasts are complementary. © 2012 Wiley Periodicals, Inc. Jrl Fut Mark 32:792‐806, 2012     

A comparative study of range‐based stock return volatility estimators for the German market

This study investigates the relative performance of various volatility estimators based on daily and intraday price ranges of 25 German equities, with the two‐scales realized volatility used as a benchmark. The empirical results show that all estimators based on daily ranges are by far superior to the classical estimator but are severely negatively biased due to discrete trading. The realized range obtained from intraday ranges performs better in terms of both bias and efficiency, although its performance still suffers from discrete trading. In these settings, the bias correcting procedure developed by Christensen and Podolskij (2007) appears to consistently outperform all other alternatives, including the scaled version of Martens and van Dijk (2007), and provides evidence of the relative advantages of the realized range. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark 32:560–586, 2012     

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     

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.     

The information content of option implied volatility surrounding the 1997 Hong Kong stock market crash

This study examines the information conveyed by options and examines their implied volatility at the time of the 1997 Hong Kong stock market crash. The author determines the efficiency of implied volatility as a predictor of future volatility by comparing it to other leading indicator candidates. These include volume and open interest of index options and futures, as well as the arbitrage basis of index futures. Using monthly, nonoverlapping data, the study reveals that implied volatility is superior to those variables in forecasting future realized volatility. The study also demonstrates that a simple signal extraction model could have produced useful warning signals prior to periods of extreme volatility. These results indicate that the options market is highly efficient informationally. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:555–574, 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     

The information content of implied volatility in light of the jump/continuous decomposition of realized volatility

In the framework of encompassing regressions, the information content of the jump/continuous components of historical volatility is assessed when implied volatility is included as an additional regressor. The authors' empirical application focuses on daily and intradaily data for the S&P100 and S&P500 indexes, and daily data for the associated VXO and VIX implied volatility indexes. The results show that the total explanatory power of the encompassing regressions barely changes when the jump/continuous components are included, although the weekly and monthly continuous components are usually significant. This evidence supports the view that implied volatility has very high information content, even when extended decompositions of past realized volatility are used. Moreover, adding GARCH‐type volatility forecasts in the regressions confirms these results. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:337–359, 2007     

Implied volatility forecasts in the grains complex

This article finds that the implied volatilities of corn, soybean, and wheat futures options 4 weeks before option expiration have significant predictive power for the underlying futures contract return volatilities through option expiration from January 1988 through September 1999. These implied volatilities also encompass the information in out‐of‐sample seasonal Glosten, Jagannathan, and Runkle (GJR;1993) volatility forecasts. Evidence also demonstrates that when corn‐implied volatility rises relative to out‐of‐sample seasonal GJR volatility forecasts, implied volatility substantially overpredicts realized volatility. However, simulations of trading rules that involve selling corn option straddles when corn‐implied volatility is high relative to out‐of‐sample GJR volatility forecasts indicate that none of the trading rules would have been significantly profitable. This finding suggests that these options are not necessarily overpriced. © 2002 Wiley Periodicals, Inc. Jrl Fut Mark 22:959–981, 2002     

Predicting financial volatility: High‐frequency time‐series forecasts vis‐à‐vis implied volatility

Recent evidence suggests option implied volatilities provide better forecasts of financial volatility than time‐series models based on historical daily returns. In this study both the measurement and the forecasting of financial volatility is improved using high‐frequency data and long memory modeling, the latest proposed method to model volatility. This is the first study to extract results for three separate asset classes, equity, foreign exchange, and commodities. The results for the S&P 500, YEN/USD, and Light, Sweet Crude Oil provide a robust indication that volatility forecasts based on historical intraday returns do provide good volatility forecasts that can compete with and even outperform implied volatility. © 2004 Wiley Periodicals, Inc. Jrl Fut Mark 24:1005–1028, 2004     

Examination of long‐term bond iShare option selling strategies

This article examines volatility trades in Lehman Brothers 20+ Year US Treasury Index iShare (TLT) options from July 2003 through May 2007. Unconditionally selling front contract strangles and straddles and holding for one month is highly profitable after transactions costs. Short‐term option selling strategies are enhanced when implied volatility is high relative to time series volatility forecasts. Risk management strategies such as stop loss orders detract from profitability, while take profit orders have only modest favorable effects on profitability. Overall, the results demonstrate that TLT option selling strategies offered attractive risk‐return tradeoffs over the sample period. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:465–489, 2010     

Value at risk and conditional extreme value theory via markov regime switching models

This study develops a new conditional extreme value theory‐based (EVT) model that incorporates the Markov regime switching process to forecast extreme risks in the stock markets. The study combines the Markov switching ARCH (SWARCH) model (which uses different sets of parameters for various states to cope with the structural changes for measuring the time‐varying volatility of the return distribution) with the EVT to model the tail distribution of the SWARCH processed residuals. The model is compared with unconditional EVT and conditional EVT‐GARCH models to estimate the extreme losses in three leading stock indices: S&P 500 Index, Hang Seng Index and Hang Seng China Enterprise Index. The study found that the EVT‐SWARCH model outperformed both the GARCH and SWARCH models in capturing the non‐normality and in providing accurate value‐at‐risk forecasts in the in‐sample and out‐sample tests. The EVTSWARCH model, which exhibits the features of measuring the volatility of a heteroscedastic financial return series and coping with the non‐normality owing to structural changes, can be an alternative measure of the tail risk. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:155–181, 2008     

基于高频数据的ARCH类模型波动预测比较分析

Realized Volatility是在高频数据的研究基础上发展起来的度量波动率的新方法。本文以上证综合指数的高频数据为研究对象,采用滚动式样本外一步预测的方法对5种ARCH类模型进行了模型预测能力的比较研究。主要结论有:(1)Realized Volatility作为解释变量加入GARCH模型后能够提高波动预测精度。(2)GARCH-RV的波动预测值为Realized Volatility的无偏估计量。(3)沪市存在波动非对称性与很长的持续性。     

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.     

Return distributions and volatility forecasting in metal futures markets: Evidence from gold,silver, and copper

The characterization of return distributions and forecast of asset‐price variability play a critical role in the study of financial markets. This study estimates four measures of integrated volatility—daily absolute returns, realized volatility, realized bipower volatility, and integrated volatility via Fourier transformation (IVFT)—for gold, silver, and copper by using high‐frequency data for the period 1999 through 2008. The distributional properties are investigated by applying recently developed jump detection procedures and by constructing financial‐time return series. The predictive ability of a GARCH (1,1) forecasting model that uses various volatility measures is also examined. Three important findings are reported. First, the magnitude of the IVFT volatility estimate is the greatest among the four volatility measures. Second, the return distributions of the three markets are not normal. However, when returns are standardized by IVFT and realized volatility, the corresponding return distributions bear closer resemblance to a normal distribution. Notably, the application of financial‐time sampling technique is helpful in obtaining a normal distribution. Finally, the IVFT and realized volatility proxies produce the smallest forecasting errors, and increasing the time frequency of estimating integrated volatility does not necessarily improve forecast accuracy. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark 31:55–80, 2011     

Volatility information implied in the term structure of VIX

This study uses multiple maturity-independent variables to examine whether the volatility information implied in the term structure of volatility index can improve the prediction of realized volatility. The empirical results for the S&P 500 index show that, in terms of both the in-sample estimation and out-of-sample forecasting, the term structure variables provide substantial incremental contribution to the models with only level variables. Our empirical results are robust to various forms of volatility, alternative ways to develop the term structure variable, the impact of macroeconomic variables, and alternative underlying assets.     

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     

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.     

Pricing VIX futures: Evidence from integrated physical and risk‐neutral probability measures

This study derives closed‐form solutions to the fair value of VIX (volatility index) futures under alternate stochastic variance models with simultaneous jumps both in the asset price and variance processes. Model parameters are estimated using an integrated analysis of integrated volatility and VIX time series from April 21, 2004 to April 18, 2006. The stochastic volatility model with price jumps outperforms for the short‐dated futures, whereas additionally including a state‐dependent volatility jump can further reduce out‐of‐sample pricing errors for other futures maturities. Finally, adding volatility jumps enhances hedging performance except for the short‐dated futures on a daily‐rebalanced basis. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:1175–1217, 2007