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     

Earnings announcement timing,uncertainty, and volatility risk premiums

We examine the relationship between firms’ quarterly earnings report timing and uncertainty before quarterly earnings announcements. Prior research provides conflicting predictions on how investor uncertainty and report timing are related. Using implied volatilities from equity options and the realized returns to straddle positions, we find evidence that uncertainty and volatility risk premiums are higher for firms that report later in the quarter. Further tests show that the increase in option premiums is unexplained by risk factors suggesting a mispricing by investors. These results are not associated with static firm-level factors and our findings are concentrated in high growth firms.     

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     

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 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     

基于异质信念的公司特质风险定价模型

文章讨论了加入异质信念后公司特质风险对预期收益率的影响。通过放宽经典Merton模型的假设条件,加入异质信念和卖空限制,重新推导了特质波动率与预期收益率之间的关系。结果表明,在投资者无法多样化投资的前提下,即使考虑了异质信念,公司特质波动率仍然进入资产定价方程,特质波动率与预期收益率之间存在正向关系。     

Stock return dynamics,option volume,and the information content of implied volatility

This article reports new empirical results on the information content of implied volatility, with respect to modeling and forecasting the volatility of individual firm returns. The 50 firms with the highest option volume on the Chicago Board Options Exchange between 1988 and 1995 are examined. First, the results indicate that the ability of implied volatility to subsume all relevant information about conditional variance depends on option trading volume. For the most active options in the sample, implied volatility reliably outperforms GARCH and subsumes all information in return shocks beyond the first lag. For these active options, implied volatility performs substantially better than indicated by the prior results of Lamoureux and Lastrapes ( 1993 ), despite significant methodological improvements in the time‐series volatility models in this study including the use of high‐frequency intraday return shocks. For the lower option‐volume firms in the sample, the performance of implied volatility deteriorates relative to time‐series volatility models. Finally, compared to a time‐series approach, the implied volatility of equity index options provides reliable incremental information about future firm‐level volatility. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:615–646, 2003     

Is volatility risk priced in the securities market? Evidence from S&P 500 index options

The authors examine whether volatility risk is a priced risk factor in securities returns. Zero‐beta at‐the‐money straddle returns of the S&P 500 index are used to measure volatility risk. It is demonstrated that volatility risk captures time variation in the stochastic discount factor. The results suggest that straddle returns are important conditioning variables in asset pricing, and investors use straddle returns when forming their expectations about securities returns. One interesting finding is that different classes of firms react differently to volatility risk. For example, small firms and value firms have negative and significant volatility coefficients, whereas big firms and growth firms have positive and significant volatility coefficients during high‐volatility periods, indicating that investors see these latter firms as hedges against volatile states of the economy. Overall, these findings have important implications for portfolio formation, risk management, and hedging strategies. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:617–642, 2007     

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     

Asymmetric pricing of implied systematic volatility in the cross‐section of expected returns

Assuming a symmetric relation between returns and innovations in implied market volatility, Ang, A., Hodrick, R., Xing, Y., and Zhang, X. (2006) find that sensitivities to changes in implied market volatility have a cross‐sectional effect on firm returns. Dennis, P., Mayhew, S., and Stivers, C. (2006), however, find an asymmetric relation between firm‐level returns and implied market volatility innovations. We incorporate this asymmetry into the cross‐sectional relation between sensitivity to volatility innovations and returns. Using both portfolio sorting and firm‐level regressions, we find that sensitivity to VIX innovations is negatively related to returns when volatility is rising, but is unrelated when it is falling. The negative relation is robust to controls for other variables, suggesting only the increase in implied market volatility is a priced risk factor. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark 31:34–54, 2011     

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 Co‐Movement of Credit Default Swap Spreads,Equity Returns and Volatility: Evidence from Asia‐Pacific Markets

We provide a comprehensive analysis of the co‐movement of credit default swap (CDS), equity, and volatility markets in four Asia‐Pacific countries at firm and index level during the period 2007–2010. First, we examine lead–lag relationships between CDS spread changes, equity returns, and changes in volatility using a vector autoregressive model. At the firm level equity returns lead changes in CDS spreads and realized volatility. However, at the index level the intertemporal linkages between the three markets are less clear‐cut. Second, we apply the measures proposed by Diebold and Yilmaz (2014) to an analysis of volatility spillovers among the CDS, equities, and volatility asset classes. The results suggest that realized volatility (at firm level) and implied volatility (at index level) are the main transmitters of cross‐market volatility spillovers. Third, we analyze the impact of various structural factors and confirm the importance of realized volatility of equity returns as a determinant of CDS spreads.     

The drift factor in biased futures index pricing models: A new look

The presence of bias in index futures prices has been investigated in various research studies. Redfield ( 11 ) asserted that the U.S. Dollar Index (USDX) futures contract traded on the U.S. Cotton Exchange (now the FINEX division of the New York Board of Trade) could be systematically arbitraged for nontrivial returns because it is expressed in so‐called “European terms” (foreign currency units/U.S. dollar). Eytan, Harpaz, and Krull ( 4 ) (EHK) developed a theoretical factor using Brownian motion to correct for the European terms and the bias due to the USDX index being expressed as a geometric average. Harpaz, Krull, and Yagil ( 5 ) empirically tested the EHK index. They used the historical volatility to proxy the EHK volatility specification. Since 1990, it has become more commonplace to use option‐implied volatility for forecasting future volatility. Therefore, we have substituted option implied volatilities into EHK's correction factor and hypothesized that the correction factor is “better” ex ante and therefore should lead to better futures model pricing. We tested this conjecture using twelve contracts from 1995 through 1997 and found that the use of implied volatility did not improve the bias correction over the use of historical volatility. Furthermore, no matter which volatility specification we used, the model futures price appeared to be mis‐specified. To investigate further, we added a simple naïve δ based on a modification of the adaptive expectations model. Repeating the tests using this naïve “drift” factor, it performed substantially better than the other two specifications. Our conclusion is that there may be a need to take a new look at the drift‐factor specification currently in use. © 2002 Wiley Periodicals, Inc. Jrl Fut Mark 22:579–598, 2002     

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     

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。     

LEVERAGED ETF IMPLIED VOLATILITIES FROM ETF DYNAMICS

The growth of the exchange‐traded fund (ETF) industry has given rise to the trading of options written on ETFs and their leveraged counterparts (LETFs). We study the relationship between the ETF and LETF implied volatility surfaces when the underlying ETF is modeled by a general class of local‐stochastic volatility models. A closed‐form approximation for prices is derived for European‐style options whose payoffs depend on the terminal value of the ETF and/or LETF. Rigorous error bounds for this pricing approximation are established. A closed‐form approximation for implied volatilities is also derived. We also discuss a scaling procedure for comparing implied volatilities across leverage ratios. The implied volatility expansions and scalings are tested in three settings: Heston, limited constant elasticity of variance (CEV), and limited SABR; the last two are regularized versions of the well‐known CEV and SABR models.     

The Breakdown of Idiosyncratic Volatility Into Expected and Unexpected Components and Its Effects on Stock Returns in Brazil

Based on studies of idiosyncratic volatility developed in the recent literature, this study analyzes its relation with expected returns through the breakdown of idiosyncratic volatility in the Brazilian stock market and presents evidence of the importance of expected idiosyncratic volatility for asset pricing. We study the impact of the expected and unexpected components of idiosyncratic volatility on the returns of shares listed on the BOVESPA between 2004 and 2011. The results show a strong positive and significant relation between expected idiosyncratic volatility and returns. This evidence is highlighted when we use unexpected idiosyncratic volatility to control for unexpected returns. Additional robustness tests, controlling for size and momentum effects, also have positive and significant coefficients, corroborating previous findings.     

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.     

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     

Corporate Hedging and the High Idiosyncratic Volatility Low Return Puzzle

The literature offers various explanations to either support or refute the Ang et al. ( 2006 ) high idiosyncratic volatility low return puzzle. Fu ( 2009 ) finds a significantly positive contemporaneous relation between return and exponential generalized autoregressive conditional heteroskedastic idiosyncratic volatility. We use corporate hedging to shed light on this puzzle. Conceptually, idiosyncratic volatility matters to investors who face limits to diversification. But limits to diversification become less relevant for firms that consistently hedge. We confirm the main finding in Fu ( 2009 ), but only for firms that do not consistently hedge. For firms that adopt a consistent hedging policy, idiosyncratic volatility, whether contemporaneous or lagged, is insignificant in Fama–MacBeth regressions, controlling for size, book‐to‐market, momentum, liquidity, and industry effects.