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     

The information content in implied idiosyncratic volatility and the cross‐section of stock returns: Evidence from the option markets

Current literature is inconclusive as to whether idiosyncratic risk influences future stock returns and the direction of the impact. Earlier studies are based on historical realized volatility. Implied volatilities from option prices represent the market's assessment of future risk and are likely a superior measure to historical realized volatility. Implied idiosyncratic volatilities on firms with traded options are used to examine the relationship between idiosyncratic volatility and future returns. A strong positive link was found between implied idiosyncratic risk and future returns. After considering the impact of implied idiosyncratic volatility, historical realized idiosyncratic volatility is unimportant. This performance is strongly tied to small size and high book‐to‐market equity firms. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28: 1013–1039, 2008     

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     

Density forecast comparisons for stock prices,obtained from high‐frequency returns and daily option prices

This paper presents the first comparison of the accuracy of density forecasts for stock prices. Six sets of forecasts are evaluated for DJIA stocks, across four forecast horizons. Two forecasts are risk‐neutral densities implied by the Black–Scholes and Heston models. The third set are historical lognormal densities with dispersion determined by forecasts of realized variances obtained from 5‐min returns. Three further sets are defined by transforming risk‐neutral and historical densities into real‐world densities. The most accurate method applies the risk transformation to the Black–Scholes densities. This method outperforms all others for 87% of the comparisons made using the likelihood criterion.     

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.     

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     

Conditional Volatility and the GARCH Option Pricing Model with Non‐Normal Innovations

On the basis of the theory of a wedge between the physical and risk‐neutral conditional volatilities in Christoffersen, P., Elkamhi, R., Feunou, B., & Jacobs, K. (2010), we develop a modification of the GARCH option pricing model with the filtered historical simulation proposed in Barone‐Adesi, G., Engle, R. F., & Mancini, L. (2008). The one‐day‐ahead conditional volatilities under physical and risk‐neutral measures are the same in the previous model, but should have been allowed to be different. Using extensive data on S&P 500 index options, our approach, which employs one‐day‐ahead risk‐neutral conditional volatility estimated from the cross‐section of the option prices (in contrast to the existing GARCH option pricing models), maintains theoretical consistency under conditional non‐normality, and improves the empirical performances. Remarkably, the risk‐neutral volatility dynamics are stable over time in this model. In addition, the comparison between the VIX index and the risk‐neutral integrated volatility economically validates our approach. © 2011 Wiley Periodicals, Inc. Jrl Fut Mark 33:1–28, 2013     

EXPLICIT IMPLIED VOLATILITIES FOR MULTIFACTOR LOCAL‐STOCHASTIC VOLATILITY MODELS

We consider an asset whose risk‐neutral dynamics are described by a general class of local‐stochastic volatility models and derive a family of asymptotic expansions for European‐style option prices and implied volatilities. We also establish rigorous error estimates for these quantities. Our implied volatility expansions are explicit; they do not require any special functions nor do they require numerical integration. To illustrate the accuracy and versatility of our method, we implement it under four different model dynamics: constant elasticity of variance local volatility, Heston stochastic volatility, three‐halves stochastic volatility, and SABR local‐stochastic volatility.     

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     

Volatility forecasts embedded in the prices of crude-oil options

This paper evaluates the ability of alternative option-implied volatility measures to forecast crude-oil return volatility. We find that a corridor implied volatility measure that aggregates information from a narrow range of option contracts consistently outperforms forecasts obtained by the popular Black–Scholes and model-free volatility expectations, as well as those generated by a realized volatility model. This measure ranks favorably in regression-based tests, delivers the lowest forecast errors under different loss functions, and generates economically significant gains in volatility timing exercises. Our results also show that the Chicago Board Options Exchange's “oil-VIX” index performs poorly, as it routinely produces the least accurate forecasts.     

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     

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     

Forecasting performance of extreme‐value volatility estimators

This study evaluates the forecasting performance of extreme‐value volatility estimators for the equity‐based Nifty Index using two‐scale realized volatility. This benchmark mitigates the effect of microstructure noise in the realized volatility. Extreme‐value estimates with relatively simple forecasting methods provide substantially better short‐term and long‐term forecasts, compared to historical volatility. The higher efficiency of extreme‐value estimators is primarily responsible for this improvement. The extent of possible improvement in forecasts is likely to be economically significant for applications like options pricing. By including extremevalue estimators, the forecasting performance of generalized autoregressive conditional heteroscedasticity (GARCH) can also be improved. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27: 1085–1105, 2007     

Persistence of volatility in futures markets

This article examines the characteristics of key measures of volatility for different types of futures contracts to provide a better foundation for modeling volatility behavior and derivative values. Particular attention is focused on analyzing how different measures of volatility affect volatility persistence relationships. Intraday realized measures of volatility are found to be more persistent than daily measures, the type of GARCH procedure used for conditional volatility analysis is critical, and realized volatility persistence is not coherent with conditional volatility persistence. Specifically, although there is a good fit between the realized and conditional volatilities, no coherence exists between their degrees of persistence, a counterintuitive finding that shows realized and conditional volatility measures are not a substitute for one another. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:571–594, 2006     

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     

The interrelation of price volatility and trading volume of currency options

This article examines the interrelations between future volatility of the U.S. dollar/British pound exchange rate and trading volume of currency options for the British pound. The future volatility of the exchange rate is approximated alternatively by implied volatility and by IGARCH volatility. The results suggest the presence of strong contemporaneous positive feedbacks between the exchange rate volatility and the trading volume of call and put options. Previous option volumes have significant predictive power with respect to the expected future volatility of the dollar/pound exchange rate. Similarly, lagged volatilities jointly have significant predictive power for option volume. Although option volume (volatility) responds somewhat differently to individual volatility (volume) terms under the two volatility measures, the overall volume‐volatility relations are broadly similar between the implied and IGARCH volatilities. The results generally support the hypothesis that the information‐based trading explains more of the trading volume in currency options on the U.S. dollar/British pound exchange rate than hedging. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:681–700, 2003     

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     

中国股市存在"特质波动率之谜"吗?

文章讨论了中国股市是否存在特质波动率之谜,实证结果表明,滞后的特质波动率并不是预期特质波动率的一个好的估计值。所谓特质波动率之谜是由于研究者错误地使用滞后的特质波动率来取代预期特质波动率而出现的伪现象。文章采用对每支股票的对数特质波动率序列建立ARMA模型的方法提取预期特质波动率,并利用横截面回归研究预期特质波动率与预期收益率之间的关系,研究结果表明两者之间存在显著的正向关系,这种正向关系即使在考虑了各种控制变量并经过稳健性检验之后仍然成立。     

Implied correlation index: A new measure of diversification

Most approaches in forecasting future correlation depend on the use of historical information as their basic information set. Recently, there have been some attempts to use the notion of “implied” correlation as a more accurate measure of future correlation. This study proposes an innovative methodology for backing‐out implied correlation measures from index options. This new measure called implied correlation index reflects the market view of the future level of the diversification in the market portfolio represented by the index. The methodology is applied to the Dow Jones Industrial Average index, and the statistical properties and the dynamics of the proposed implied correlation measure are examined. The evidence of this study indicates that the implied correlation index fluctuates substantially over time and displays strong dynamic dependence. Moreover, there is a systematic tendency for the implied correlation index to increase when the market index returns decrease and/or the market volatility increases, indicating limited diversification when it is needed most. Finally, the forecast performance of the implied correlation index is assessed. Although the implied correlation index is a biased forecast of realized correlation, it has a high explanatory power, and it is orthogonal to the information set compared to a historical forecast. © 2005 Wiley Periodicals, Inc. Jrl Fut Mark 25:171–197, 2005     

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