Forecasting and trading on the VIX futures market: A neural network approach based on open to close returns and coincident indicators

Previous work has highlighted the difficulty of obtaining accurate and economically significant predictions of VIX futures prices. We show that both low prediction errors and a significant amount of profitability can be obtained by using a neural network model to predict VIX futures returns. In particular, we focus on open-to-close returns (OTCRs) and consider intraday trading strategies, taking into account non-lagged exogenous variables that closely reflect the information possessed by traders at the time when they decide to invest. The neural network model with only the most recent exogenous variables (namely, the return on the Indian BSESN index) is superior to an unconstrained specification with ten lagged and coincident regressors, which is actually a form of weak efficiency involving markets of different countries. Moreover, the neural network turns out to be more profitable than either a logistic specification or heterogeneous autoregressive models.     

Forecasting returns in the VIX futures market

This paper introduces a new forecasting model for VIX futures returns. The model is structural in nature and parsimonious, and contains parameters that are relatively easy to estimate. The forecasts of next day VIX futures returns based on this model are superior to those produced by a linear forecasting model that uses the same set of predictors. Moreover, the profits to a market-timing model based on the proposed forecasts are statistically and economically significant, and are robust to both the method used for adjusting for risk and transaction costs (up to around 15 basis points). In contrast, the forecasts generated by the linear forecasting model are not.     

Pure jump models for pricing and hedging VIX derivatives

Recent non-parametric statistical analysis of high-frequency VIX data (Todorov and Tauchen, 2011) reveals that VIX dynamics is a pure jump semimartingale with infinite jump activity and infinite variation. To our best knowledge, existing models in the literature for pricing and hedging VIX derivatives do not have these features. This paper fills this gap by developing a novel class of parsimonious pure jump models with such features for VIX based on the additive time change technique proposed in Li et al., 2016a, Li et al., 2016b. We time change the 3/2 diffusion by a class of additive subordinators with infinite activity, yielding pure jump Markov semimartingales with infinite activity and infinite variation. These processes have time and state dependent jumps that are mean reverting and are able to capture stylized features of VIX. Our models take the initial term structure of VIX futures as input and are analytically tractable for pricing VIX futures and European options via eigenfunction expansions. Through calibration exercises, we show that our model is able to achieve excellent fit for the VIX implied volatility surface which typically exhibits very steep skews. Comparison to two other models in terms of calibration reveals that our model performs better both in-sample and out-of-sample. We explain the ability of our model to fit the volatility surface by evaluating the matching of moments implied from market VIX option prices. To hedge VIX options, we develop a dynamic strategy which minimizes instantaneous jump risk at each rebalancing time while controlling transaction cost. Its effectiveness is demonstrated through a simulation study on hedging Bermudan style VIX options.     

Forecasting VIX using two-component realized EGARCH model

In this paper, we propose the two-component realized EGARCH (REGARCH-2C) model, which accommodates the high-frequency information and the long memory volatility through the realized measure of volatility and the component volatility structure, to forecast VIX. We obtain the risk-neutral dynamics of the REGARCH-2C model and derive the corresponding model-implied VIX formula. The parameter estimates of the REGARCH-2C model are obtained via the joint maximum likelihood estimation using observations on the returns, realized measure and VIX. Our empirical results demonstrate that the proposed REGARCH-2C model provides more accurate VIX forecasts compared to a variety of competing models, including the GARCH, GJR-GARCH, nonlinear GARCH, Heston–Nandi GARCH, EGARCH, REGARCH and two two-component GARCH models. This result is found to be robust to alternative realized measure. Our empirical evidence highlights the importance of incorporating the realized measure as well as the component volatility structure for VIX forecasting.     

VIX forecasting based on GARCH-type model with observable dynamic jumps: A new perspective

This paper proposes to study VIX forecasting based on discrete time GARCH-type model with observable dynamic jump intensity by incorporating high frequency information (DJI-GARCH model). The analytical expression is obtained by deducing the forward iteration relations of vector composed of conditional variance and jump intensity, and parameters are estimated via maximum likelihood functions. To compare the pricing ability, we also present VIX forecasting under four simple GARCH-type models. Results find that DJI-GARCH model outperforms other GARCH-type models for the whole sample and stable period in terms of both in-sample and out-of-sample forecasting, and for the in-sample forecasting during crisis period. This indicates that incorporating both realized bipower and jump variations, and combining VIX information in the estimation can obtain more accuracy forecasting. However, the out-of-sample forecasting using parameters estimated from crisis period shows that GARCH and GJR-GARCH models performs relatively better, which reminds us to be cautious when making out-of-sample prediction.     

Consistent pricing of VIX options with the Hawkes jump-diffusion model

This paper presents a valuation of VIX options employing a Hawkes jump-diffusion model that captures the clustering pattern of jumps observed extensively in the financial markets. In the consistent framework, the valuation problem of VIX options is solved efficiently via the Fourier cosine expansion (COS) method. The Monte Carlo (MC) simulations are carried out to demonstrate the reliability and efficiency of the COS method. Furthermore, a sensitivity analysis is performed to show how option prices response to different parameters associated with jump clustering. Finally, empirical studies are conducted to provide evidence to support our jump specification in matching the VIX option surface.     

Interrelations in market fears of U.S. and European equity markets

We examine interdependence between the implied volatilities of U.S. and five European markets in an integrated multivariate system that allows interactions in the first and second moments of volatility processes. Our results find significant interactions in the variance-covariance matrix of VIX and European volatilities which persist and facilitate risk transmission. Changes in U.S. and Eurozone volatilities are important drivers of risk shocks in European markets. VIX and European volatilities have predictive ability for each other. Further, VIX shocks contribute significantly to the prediction error of European risk shocks, but not vice versa. Risk transmission from U.K. markets to U.S. and European markets intensified around the Brexit vote. Also, VIX shocks added significantly more to European risks during the global financial crisis. Our results highlight the potential weakness of risk transmission models that ignore the second-moment risk transmission channel and have implications for volatility trades, portfolio diversification strategies, and hedging the cross-market risks.     

Are VIX futures prices predictable? An empirical investigation

This paper investigates whether volatility futures prices per se can be forecasted by studying the fast-growing VIX futures market. To this end, alternative model specifications are employed. Point and interval out-of-sample forecasts are constructed and evaluated under various statistical metrics. Next, the economic significance of the forecasts obtained is also assessed by performing trading strategies. Only weak evidence of statistically predictable patterns in the evolution of volatility futures prices is found. No trading strategy yields economically significant profits. Hence, the hypothesis that the VIX volatility futures market is informationally efficient cannot be rejected.     

The empirical linkages among market returns,return volatility,and trading volume: Evidence from the S&P 500 VIX Futures

The purpose of this study is to examine the relationships between return and trading volume as well as between return volatility and trading volume by analyzing the asymmetric relationships of contemporaneity and lead-lags between these factors for the S&P 500 VIX Futures Index. We apply the threshold model with the GJR-GARCH framework for empirical analysis herein. The main findings demonstrate that the threshold effects exist in both the contemporaneous and lead-lag relationships between return-volume and volatility-volume. Moreover, the delayed effects of a one-trading-day lag through to three-trading-day lags exist from trading volume to returns and return volatility. Larger trading volume is beneficial for investors to gain returns, but it also leads to higher volatility. The implication of our findings offers a suggestion as to the opportune timing for investors to buy S&P 500 VIX Futures.     

Day-of-the-week effect on the VIX. A parsimonious representation

The study of significant deterministic seasonal patterns in financial asset returns is of high importance to academia and investors. This paper analyzes the presence of seasonal daily patterns in the VIX and S&P 500 returns series using a trigonometric specification. First, we show that, given the isomorphism between the trigonometrical and alternative seasonality representations (i.e., daily dummies), it is possible to test daily seasonal patterns by employing a trigonometrical representation based on a finite sum of weighted sines and cosines. We find a potential evolutive seasonal pattern in the daily VIX that is not in the daily S&P 500 log-returns series. In particular, we find an inverted Monday effect in the VIX level and changes in the VIX, and a U-shaped seasonal pattern in the changes in the VIX when we control for outliers. The trigonometrical representation is more robust to outliers than the one commonly used by literature, but it is not immune to them. Finally, we do not find a day-of-the-week effect in S&P 500 returns series, which suggests the presence of a deterministic seasonal pattern in the relation between VIX and S&P 500 returns.     

The VIX,the variance premium and stock market volatility

We decompose the squared VIX index, derived from US S&P500 options prices, into the conditional variance of stock returns and the equity variance premium. We evaluate a plethora of state-of-the-art volatility forecasting models to produce an accurate measure of the conditional variance. We then examine the predictive power of the VIX and its two components for stock market returns, economic activity and financial instability. The variance premium predicts stock returns while the conditional stock market variance predicts economic activity and has a relatively higher predictive power for financial instability than does the variance premium.     

Pricing VIX options with stochastic volatility and random jumps

This study presents an analytical exact solution for the price of VIX options under stochastic volatility model with simultaneous jumps in the asset price and volatility processes. We shall demonstrate that our new pricing formula can be used to efficiently compute the numerical values of a VIX option. While we also show that the numerical results obtained from our formula consistently match those obtained from Monte Carlo simulation perfectly as a verification of the correctness of our formula, numerical evidence is offered to illustrate that the correctness of the formula proposed in Lin and Chang (J Futur Markets 29(6), 523–543, 2009) is in serious doubt. Moreover, some important and distinct properties of VIX options (e.g., put-call parity, hedging ratios) are also examined and discussed.     

Impact of uncertainty on high frequency response of the U.S. stock markets to the Fed's policy surprises

This paper examines the impact of uncertainty on estimated response of stock returns to U.S. monetary policy surprise. This is motivated by the Lucas island model which suggests an inverse relationship between the effectiveness of a policy and the level of uncertainty in the economy. Using high frequency daily data from the Federal funds futures market, we first estimate the response of S&P 500 stock returns to monetary policy surprises within the time varying parameter (TVP) model. We then analyze the relationship of these time varying estimates with the benchmark VIX index and alternative measures of uncertainty. Evidence suggests a significant negative relationship between the level of uncertainty and the time varying response of S&P 500 stock returns to unanticipated changes in the interest rate. Thus, at higher levels of uncertainty the impact of monetary policy shocks on stock markets is lower. The results are robust to different measures of uncertainty.     

The impact of VIX on China’s financial market: A new perspective based on high-dimensional and time-varying methods

Based on the new perspective of high-dimensional and time-varying methods, this paper analyzes the contagion effects of US financial market volatility on China’s nine financial sub-markets. The results show evidence of non-linear Granger causality from the US financial volatility (VIX) to the China’s financial markets. Increased US financial volatility has a negative next-day impact on the stock, bond, fund, interest rate, foreign exchange, industrial product and agricultural product markets, and a positive next-day impact on the gold and real estate markets. US financial volatility has the greatest impact on industrial product market, following by stock, agricultural product, fund, real estate, bond, gold, foreign exchange, and interest rates. Major risk events such as the global financial crisis can cause an enhanced contagion effect of US financial volatility to China's financial markets. This paper supports the achievements of China's actions to prevent and resolve major financial risks in the period of the COVID-19 epidemic.     

Forecasting the volatility of asset returns: The informational gains from option prices

A new class of forecasting models is proposed that extends the realized GARCH class of models through the inclusion of option prices to forecast the variance of asset returns. The VIX is used to approximate option prices, resulting in a set of cross-equation restrictions on the model’s parameters. The full model is characterized by a nonlinear system of three equations containing asset returns, the realized variance, and the VIX, with estimation of the parameters based on maximum likelihood methods. The forecasting properties of the new class of forecasting models, as well as a number of special cases, are investigated and applied to forecasting the daily S&P500 index realized variance using intra-day and daily data from September 2001 to November 2017. The forecasting results provide strong support for including the realized variance and the VIX to improve variance forecasts, with linear conditional variance models performing well for short-term one-day-ahead forecasts, whereas log-linear conditional variance models tend to perform better for intermediate five-day-ahead forecasts.     

Investor sentiment and energy futures predictability: Evidence from Feasible Quasi Generalized Least Squares

Contributing to the budding literature on how emotional and sentimental actions impact the performance of financial markets, this study examines the predictability of energy futures prices with investors’ sentiments. In particular, we examine which of the three (neutral, bear and bull) investors’ sentiments offer accurate forecast information on four energy futures prices. Using the predictability test proposed by Westerlund and Narayan (2015), we discover that all the forms of investors’ sentiments are significant predictors of the movements in energy futures prices. However, the bear sentiments outshine other variants in the forecast of crude oil futures prices, while the bull sentiments provide the most accurate forecast information for the remaining energy futures prices, namely heating oil, gasoline and natural gas. We also find this evidence consistent even when asymmetries are considered in the predictability models. Among other implications of these findings, investors in energy futures and portfolio managers are expected to consider often emotional perceptions in their portfolio constructions and the predictability of future gains.     

Extreme risk transmission channels between the stock index futures and spot markets: Evidence from China

We develop a skewness-dependent multivariate conditional autoregressive value at risk model (SDMV-CAViaR) to detect the extreme risk transmission channels between the Chinese stock index futures and spot markets. The proposed SDMV-CAViaR model improves the forecast performance of extreme risk by introducing the high-frequency realized skewness. Specifically, the realized skewness has a significant impact on the spillovers, but the realized volatility and realized kurtosis do not, which implies that the jump component plays an important role in extreme risk spillovers. The empirical results indicate there are bidirectional extreme risk spillovers between the stock index futures and spot markets, the decline of one market has direct and indirect channels to exacerbate the extreme risk of the other market. Firstly, the market decline will directly increase the extreme risk of related markets by decreasing market returns. Besides, the decline will indirectly increase the extreme risk by increasing the negative realized skewness and extreme risk spillovers.     

Aggregate volatility expectations and threshold CAPM

We propose a volatility-based capital asset pricing model (V-CAPM) in which asset betas change discretely with respect to changes in investors’ expectations regarding near-term aggregate volatility. Using a novel measure to proxy uncertainty about expected changes in aggregate volatility, i.e. monthly range of the VIX index (RVIX), we find that portfolio betas change significantly when uncertainty about aggregate volatility expectations is beyond a certain threshold level. Due to changes in their market betas, small and value stocks are perceived as riskier than their big and growth counterparts in bad times, when uncertainty about aggregate volatility expectations is high. The proposed model yields a positive and significant market risk premium during periods when investors do not expect significant uncertainty in near-term aggregate volatility. Our findings support a volatility-based time-varying risk explanation.     

TIPS and the VIX: Spillovers from Financial Panic to Breakeven Inflation in an Automated,Nonlinear Modeling Framework

This paper examines the determinants of the breakeven inflation rate (BEI) on U.S. Treasury Inflation Protected Securities. After controlling for several measures of liquidity, inflation expectations and inflation uncertainty; financial fear itself (proxied with the Volatility Index or VIX) remains a primary influence on BEI. To delve into the mechanism underlying this association, the VIX is decomposed, using intraday data, into conditional variance and the variance premium capturing risk aversion. Aside from the 2008 crisis, most of the effect emanated from the variance premium. Following the crisis, indicators of bank insolvency risk gain prominence as well. Lastly, an automated nonlinear model finds convex effects of variance, and diminishing returns to insolvency risk and liquidity.     

Do Analysts Strategically Employ Cash Flow Forecast Revisions to Offset Negative Earnings Forecast Revisions?

We investigate whether analysts use cash flow forecasts to reduce the impact of earnings forecast revisions (EFRs) on market participants. In particular, we focus on conflict between an analyst's concurrent cash flow and earnings forecast revisions. We hypothesize and find that analysts are more likely to issue a positive cash flow forecast revision when they issue a negative earnings forecast revision concurrently, but not the opposite, particularly for Fortune 500 firms. Furthermore, our supplementary analyses suggest that (1) some analysts optimistically bias cash flow forecasts when they issue negative earnings forecast revisions; (2) the market pays less attention to the historical accuracy of analyst cash flow forecasts, so analysts have some latitude to present their cash flow forecasts in an optimistic way; and (3) the market reacts mainly to the direction, not the magnitude, of cash flow forecast revisions. Overall, these findings suggest that analysts may strategically use cash flow forecasts in conjunction with earnings forecasts to maintain good management relationships.