A dimension-invariant cascade model for VIX futures

We propose a new stochastic volatility model by allowing for a cascading structure of volatility components. The model, under a minor assumption, allows us to add as many components as desired with no additional parameters, effectively defeating the curse of dimensionality often encountered in traditional models. We derive a semi-closed-form solution to the VIX futures price, and find that our six-factor model with only six parameters can closely fit spot VIX and VIX futures prices from 2004 to 2015 and produce out-of-sample pricing errors of magnitudes similar to those of in-sample errors.     

Improving volatility prediction and option valuation using VIX information: A volatility spillover GARCH model

We develop a new generalized autoregressive conditional heteroskedasticity (GARCH) model that accounts for the information spillover between two markets. This model is used to detect the usefulness of the CBOE volatility index (VIX) for improving the performance of volatility forecasting and option pricing. We find the significant ability of VIX to predict stock volatility both in-sample and out-of-sample. VIX information also helps to greatly reduce the option pricing error. The proposed volatility spillover GARCH model performs better than the related approaches proposed by Kanniainen et al. (2014, J Bank Finance, 43, pp. 200-211) and P. Christoffersen et al. (2014, J Financ Quant Anal, 49, pp. 663–697).     

VIX term structure and VIX futures pricing with realized volatility

Using an extended LHARG model proposed by Majewski et al. (2015, J Econ, 187, 521–531), we derive the closed-form pricing formulas for both the Chicago Board Options Exchange VIX term structure and VIX futures with different maturities. Our empirical results suggest that the quarterly and yearly components of lagged realized volatility should be added into the model to capture the long-term volatility dynamics. By using the realized volatility based on high-frequency data, the proposed model provides superior pricing performance compared with the classic Heston–Nandi GARCH model under a variance-dependent pricing kernel, both in-sample and out-of-sample. The improvement is more pronounced during high volatility periods.     

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.     

基于跳跃、好坏波动率的混频已实现EGARCH模型的波动率预测与风险度量

为探究资产价格的跳跃行为和收益波动的非对称效应对波动率预测的影响,以高频数据建模为视角,基于跳跃、好坏波动率将Realized EGARCH-MIDAS模型进行拓展,以提升模型的波动率预测能力与风险度量效果。运用拓展后的模型,以沪深300指数价格高频数据为样本进行实证分析,探究中国股票市场的波动性规律,并采用似然函数、信息准则和基于损失函数的DM与MCS等检验方法,综合比较了改进前后的模型对波动率及风险值的预测效果。实证结果显示：(1)沪深300指数收益的长期波动主要来源于连续波动而非跳跃波动,且受正连续波动影响更大,而负跳跃对波动具有明显的负向冲击;(2)文章提出的拓展模型均能更好地捕捉波动率的长记忆性,在样本内估计和样本外预测上也都有更好的表现,其中同时考虑跳跃与非对称影响的Realized EGARCH-MIDAS-RSJ拓展模型拥有最优的估计及预测效果。     

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.     

Fractals or I.I.D.: Evidence of long-range dependence and heavy tailedness from modeling German equity market returns

Several studies find that the return volatility of stocks tends to exhibit long-range dependence, heavy tails, and clustering. Because stochastic processes with self-similarity possess long-range dependence and heavy tails, it has been suggested that self-similar processes be employed to capture these characteristics in return volatility modeling. In this paper, we find using high-frequency data that German stocks do exhibit these stylized facts. Using one of the typical self-similar processes, fractional stable noise, we empirically compare this process with several alternative distributional assumptions in either fractal form or I.I.D. form (i.e., normal distribution, fractional Gaussian noise, generalized extreme value distribution, generalized Pareto distribution, and stable distribution) for modeling German equity market volatility. The empirical results suggest that fractional stable noise dominates these alternative distributional assumptions both in in-sample modeling and out-of-sample forecasting. Our findings suggest that models based on fractional stable noise perform better than models based on the Gaussian random walk, the fractional Gaussian noise, and the non-Gaussian stable random walk.     

Asymmetric covariance in spot‐futures markets

This article studies how the spot‐futures conditional covariance matrix responds to positive and negative innovations. The main results of the article are achieved by obtaining the Volatility Impulse Response Function (VIRF) for asymmetric multivariate GARCH structures, extending Lin (1997) findings for symmetric GARCH models. This theoretical result is general and can be applied to analyze covariance dynamics in any financial system. After testing how multivariate GARCH models clean up volatility asymmetries, the Asymmetric VIRF is computed for the Spanish stock index IBEX‐35 and its futures contract. The empirical results indicate that the spot‐futures variance system is more sensitive to negative than positive shocks, and that spot volatility shocks have much more impact on futures volatility than vice versa. Additionally, evidence is obtained showing that optimal hedge ratios are insensitive to the well‐known asymmetric volatility behavior in stock markets. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:1019–1046, 2003     

The predictability of carbon futures volatility: New evidence from the spillovers of fossil energy futures returns

In this paper, we find new evidence for the carbon futures volatility prediction by using the spillovers of fossil energy futures returns as a powerful predictor. The in-sample results show that the spillovers have a significantly positive effect on carbon futures volatility. From the out-of-sample analysis with various loss functions, we find that fossil energy return spillovers significantly outperform the benchmark and show better forecasting performance than the competing models using dimension reduction, variable selection, and combination approaches. The predictive ability of the spillovers also holds in long-term forecasting and does not derive from other carbon-related variables. It can bring substantial economic gains in the portfolio exercise within carbon futures. Finally, we provide economic explanations on the predictive ability of the fossil energy return spillover by the channels of the carbon emission uncertainty and the investor sentiment on the warming climate.     

Market inefficiencies surrounding energy announcements

We use sequential energy inventory announcements to shed new light on the informational efficiency of financial markets. Our findings provide clear evidence of inefficiency in crude oil futures and stock markets. This inefficiency can be exploited by sophisticated traders. We examine the effect of market liquidity on the efficient incorporation of information in this setting. We also construct a predictor that can predict inventory surprises and preannouncement returns in-sample and out-of-sample. Finally, we develop a combination forecast that can be used as a proxy for market expectations of oil inventory announcements.     

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.     

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.     

A novel approach to portfolio selection using news volume and sentiment

In this study, we develop a novel approach to portfolio diversification by integrating information on news volume and sentiment with the k-nearest neighbors (kNN) algorithm. Our empirical analysis indicates that high news volume contributes to portfolio risk, whereas news sentiment contributes to portfolio return. Based on these findings, we propose a kNN algorithm for portfolio selection. Our in-sample and out-of-sample tests suggest that the proposed kNN portfolio selection approach outperforms the benchmark index portfolio. Overall, we show that incorporating news volume and sentiment into portfolio selection can enhance portfolio performance by improving returns and reducing risk.     

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     

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     

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     

Predicting the Price Effect of Mergers with Polynomial Logit Demand

We propose a polynomial logit model to quantify the price effects of mergers in a static Nash setting. The proposed model is parsimonious in parameters and is shown to have excellent predictive power, rivaling the in-sample and out-of-sample predictive accuracy of the widely-used AIDS model.The analysis, using actual scanner data on bread sales, demonstrates that a linear logit model is likely to over-estimate the merger price effect.     

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。     

Stochastic multifactor models in risk management of energy futures

We adopt Schwartz and Smith's model to calculate risk measures of Brent oil and light sweet crude oil (WTI) futures contracts and Mirantes, Poblacion, and Serna's model to calculate risk measures of natural gas, gasoil, heating oil, RBOB gasoline, PJM Western Hub peak, and off-peak electricity futures contracts. The models generate well in-sample goodness of fit and satisfactory out-of-sample Value-at-Risk and expected shortfall forecasts for all the eight of the analyzed commodities. A simple and flexible estimation method improving upon existing estimation methods is developed.     

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