Forecasting crude oil price volatility

We use high-frequency intra-day realized volatility data to evaluate the relative forecasting performances of various models that are used commonly for forecasting the volatility of crude oil daily spot returns at multiple horizons. These models include the RiskMetrics, GARCH, asymmetric GARCH, fractional integrated GARCH and Markov switching GARCH models. We begin by implementing Carrasco, Hu, and Ploberger’s (2014) test for regime switching in the mean and variance of the GARCH(1, 1), and find overwhelming support for regime switching. We then perform a comprehensive out-of-sample forecasting performance evaluation using a battery of tests. We find that, under the MSE and QLIKE loss functions: (i) models with a Student’s t innovation are favored over those with a normal innovation; (ii) RiskMetrics and GARCH(1, 1) have good predictive accuracies at short forecast horizons, whereas EGARCH(1, 1) yields the most accurate forecasts at medium horizons; and (iii) the Markov switching GARCH shows a superior predictive accuracy at long horizons. These results are established by computing the equal predictive ability test of Diebold and Mariano (1995) and West (1996) and the model confidence set of Hansen, Lunde, and Nason (2011) over the entire evaluation sample. In addition, a comparison of the MSPE ratios computed using a rolling window suggests that the Markov switching GARCH model is better at predicting the volatility during periods of turmoil.     

Forecasting cryptocurrency volatility

This paper studies the behavior of cryptocurrencies’ financial time series, of which Bitcoin is the most prominent example. The dynamics of these series are quite complex, displaying extreme observations, asymmetries, and several nonlinear characteristics that are difficult to model and forecast. We develop a new dynamic model that is able to account for long memory and asymmetries in the volatility process, as well as for the presence of time-varying skewness and kurtosis. The empirical application, carried out on 606 cryptocurrencies, indicates that a robust filter for the volatility of cryptocurrencies is strongly required. Forecasting results show that the inclusion of time-varying skewness systematically improves volatility, density, and quantile predictions at different horizons.     

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.     

Forecasting realized variance measures using time-varying coefficient models

This paper considers the problem of forecasting realized variance measures. These measures are highly persistent estimates of the underlying integrated variance, but are also noisy. Bollerslev, Patton and Quaedvlieg (2016), Journal of Econometrics 192(1), 1–18 exploited this so as to extend the commonly used heterogeneous autoregressive (HAR) by letting the model parameters vary over time depending on the estimated measurement error variances. We propose an alternative specification that allows the autoregressive parameters of HAR models to be driven by a latent Gaussian autoregressive process that may also depend on the estimated measurement error variance. The model parameters are estimated by maximum likelihood using the Kalman filter. Our empirical analysis considers the realized variances of 40 stocks from the S&P 500. Our model based on log variances shows the best overall performance and generates superior forecasts both in terms of a range of different loss functions and for various subsamples of the forecasting period.     

Stochastic volatility with leverage: Fast and efficient likelihood inference

This paper is concerned with the Bayesian analysis of stochastic volatility (SV) models with leverage. Specifically, the paper shows how the often used Kim et al. [1998. Stochastic volatility: likelihood inference and comparison with ARCH models. Review of Economic Studies 65, 361–393] method that was developed for SV models without leverage can be extended to models with leverage. The approach relies on the novel idea of approximating the joint distribution of the outcome and volatility innovations by a suitably constructed ten-component mixture of bivariate normal distributions. The resulting posterior distribution is summarized by MCMC methods and the small approximation error in working with the mixture approximation is corrected by a reweighting procedure. The overall procedure is fast and highly efficient. We illustrate the ideas on daily returns of the Tokyo Stock Price Index. Finally, extensions of the method are described for superposition models (where the log-volatility is made up of a linear combination of heterogenous and independent autoregressions) and heavy-tailed error distributions (student and log-normal).     

A discrete-time model for daily S & P500 returns and realized variations: Jumps and leverage effects

We develop an empirically highly accurate discrete-time daily stochastic volatility model that explicitly distinguishes between the jump and continuous-time components of price movements using nonparametric realized variation and Bipower variation measures constructed from high-frequency intraday data. The model setup allows us to directly assess the structural inter-dependencies among the shocks to returns and the two different volatility components. The model estimates suggest that the leverage effect, or asymmetry between returns and volatility, works primarily through the continuous volatility component. The excellent fit of the model makes it an ideal candidate for an easy-to-implement auxiliary model in the context of indirect estimation of empirically more realistic continuous-time jump diffusion and Lévy-driven stochastic volatility models, effectively incorporating the interdaily dependencies inherent in the high-frequency intraday data.     

The impact of sentiment and attention measures on stock market volatility

We analyze the impact of sentiment and attention variables on the stock market volatility by using a novel and extensive dataset that combines social media, news articles, information consumption, and search engine data. We apply a state-of-the-art sentiment classification technique in order to investigate the question of whether sentiment and attention measures contain additional predictive power for realized volatility when controlling for a wide range of economic and financial predictors. Using a penalized regression framework, we identify the most relevant variables to be investors’ attention, as measured by the number of Google searches on financial keywords (e.g. “financial market” and “stock market”), and the daily volume of company-specific short messages posted on StockTwits. In addition, our study shows that attention and sentiment variables are able to improve volatility forecasts significantly, although the magnitudes of the improvements are relatively small from an economic point of view.     

Forecasting realized volatility of agricultural commodities

We forecast the realized and median realized volatility of agricultural commodities using variants of the heterogeneous autoregressive (HAR) model. We obtain tick-by-tick data on five widely-traded agricultural commodities (corn, rough rice, soybeans, sugar, and wheat) from the CME/ICE. Real out-of-sample forecasts are produced for between 1 and 66 days ahead. Our in-sample analysis shows that the variants of the HAR model which decompose volatility measures into their continuous path and jump components and incorporate leverage effects offer better fitting in the predictive regressions. However, we demonstrate convincingly that such HAR extensions do not offer any superior predictive ability in their out-of-sample results, since none of these extensions produce significantly better forecasts than the simple HAR model. Our results remain robust even when we evaluate them in a Value-at-Risk framework. Thus, there is no benefit from including more complexity, related to the volatility decomposition or relative transformations of the volatility, in the forecasting models.     

Forecasting risk measures using intraday and overnight information

Volatility forecasts are important for a number of practical financial decisions, such as those related to risk management. When working with high-frequency data from markets that operate during a reduced time, an approach to deal with the overnight return volatility is needed. In this context, we use heterogeneous autoregressions (HAR) to model the variation associated with the intraday activity, with distinct realized measures as regressors, and, to model the overnight returns, we use augmented GARCH type models. Then, we combine the HAR and GARCH models to generate forecasts for the total daily return volatility. In an empirical study, for returns on six international stock indices, we analyze the separate modeling approach in terms of its out-of-sample forecasting performance of daily volatility, Value-at-Risk and Expected Shortfall relative to standard models from the literature. In particular, the overall results are favorable for the separate modeling approach in comparison with some HAR models based on realized variance measures for the whole day and the standard GARCH model.     

Forecasting volatility and co-volatility of crude oil and gold futures: Effects of leverage,jumps, spillovers,and geopolitical risks

To forecast the covariance matrix for the returns of crude oil and gold futures, this paper examines the effects of leverage, jumps, spillovers, and geopolitical risks by using their respective realized covariance matrices. To guarantee the positive definiteness of the forecasts, we consider the full BEKK structure on the conditional Wishart model. By the specification, we can flexibly divide the direct and spillover effects of volatility feedback, negative returns, and jumps. The empirical analysis indicates the benefits of accommodating the spillover effects of negative returns, and the geopolitical risks indicator for modeling and forecasting the covariance matrix.     

Realized volatility forecasting: Robustness to measurement errors

In this paper, we suggest how to handle the issue of the heteroskedasticity of measurement errors when specifying dynamic models for the conditional expectation of realized variance. We show that either adding a GARCH correction within an asymmetric extension of the $\mathsf{HAR}$  class ($\mathsf{AHAR}$-$\mathsf{GARCH}$), or working within the class of asymmetric multiplicative error models ($\mathsf{AMEM}$) greatly reduces the need for quarticity/quadratic terms to capture attenuation bias. This feature in $\mathsf{AMEM}$ can be strengthened by considering regime specific dynamics. Model Confidence Sets confirm this robustness both in- and out-of-sample for a panel of 28 big caps and the S&P500 index.     

A novel cluster HAR-type model for forecasting realized volatility

This paper proposes a cluster HAR-type model that adopts the hierarchical clustering technique to form the cascade of heterogeneous volatility components. In contrast to the conventional HAR-type models, the proposed cluster models are based on the relevant lagged volatilities selected by the cluster group Lasso. Our simulation evidence suggests that the cluster group Lasso dominates other alternatives in terms of variable screening and that the cluster HAR serves as the top performer in forecasting the future realized volatility. The forecasting superiority of the cluster models are also demonstrated in an empirical application where the highest forecasting accuracy tends to be achieved by separating the jumps from the continuous sample path volatility process.     

The role of oil futures intraday information on predicting US stock market volatility

This study investigates the role of oil futures price information on forecasting the US stock market volatility using the HAR framework. In-sample results indicate that oil futures intraday information is helpful to increase the predictability. Moreover, compared to the benchmark model, the proposed models improve their predictive ability with the help of oil futures realized volatility. In particular, the multivariate HAR model outperforms the univariate model. Accordingly, considering the contemporaneous connection is useful to predict the US stock market volatility. Furthermore, these findings are consistent across a variety of robust checks.     

Adding dummy variables: A simple approach for improved volatility forecasting in electricity market

This study used dummy variables to measure the influence of day-of-the-week effects and structural breaks on volatility. Considering day-of-the-week effects, structural breaks, or both, we propose three classes of HAR models to forecast electricity volatility based on existing HAR models. The estimation results of the models showed that day-of-the-week effects only improve the fitting ability of HAR models for electricity volatility forecasting at the daily horizon, whereas structural breaks can improve the in-sample performance of HAR models when forecasting electricity volatility at daily, weekly, and monthly horizons. The out-of-sample analysis indicated that both day-of-the-week effects and structural breaks contain additional ex ante information for predicting electricity volatility, and in most cases, dummy variables used to measure structural breaks contain more out-of-sample predictive information than those used to measure day-of-the-week effects. The out-of-sample results were robust across three different methods. More importantly, we argue that adding dummy variables to measure day-of-the-week effects and structural breaks can improve the performance of most other existing HAR models for volatility forecasting in the electricity market.     

Volatility swaps and volatility options on discretely sampled realized variance

Volatility swaps and volatility options are financial products written on discretely sampled realized variance. Actively traded in over-the-counter markets, these products are often priced by continuously sampled approximations to simplify the computations. This paper presents an analytical approach to efficiently and accurately price discretely sampled volatility derivatives, under a general stochastic volatility model. We first obtain an accurate approximation for the characteristic function of the discretely sampled realized variance. This characteristic function is then applied to price discrete volatility derivatives through either semi-analytical pricing formulae (up to an inverse Fourier transform) or an efficient Fourier-cosine series method. Numerical experiments show that our approximation is more accurate in comparison to the approximations in the literature. We remark that although discretely sampled variance swaps and options are usually more expensive than their continuously sampled counterparts, discretely sampled volatility swaps are more prone to be cheaper than the continuously sampled counterparts. An analysis is then provided to explain why this is the case in general for realistic contract specifications and reasonable model parameters.     

Identification of volatility proxies as expectations of squared financial returns

Volatility proxies like realised volatility (RV) are extensively used to assess the forecasts of squared financial returns produced by volatility models. But are volatility proxies identified as expectations of the squared return? If not, then the results of these comparisons can be misleading, even if the proxy is unbiased. Here, a tripartite distinction is introduced between strong, semi-strong, and weak identification of a volatility proxy as an expectation of the squared return. The definition implies that semi-strong and weak identification can be studied and corrected for via a multiplicative transformation. Well-known tests can be used to check for identification and bias, and Monte Carlo simulations show that they are well sized and powerful—even in fairly small samples. As an illustration, 12 volatility proxies used in three seminal studies are revisited. Half of the proxies do not satisfy either semi-strong or weak identification, but their corrected transformations do. It is then shown how correcting for identification can change the rankings of volatility forecasts.     

Reexamining the time-varying volatility spillover effects: A Markov switching causality approach

This paper intends to examine the volatility spillover effect between selective developed markets including U.S., U.K., Germany, Japan and Hong Kong over the sample period from 1996 to 2011. We introduce a Markov switching causality method to model the potential instability of volatility spillover relationships over market tranquil or turmoil periods. This method is more flexible as no prior information on the changing points or size of sample window is needed. From the empirical results, we find the evidence of the existence of spillover effects among most markets, and the bilateral volatility spillover effects are more prominent over turmoil or crisis episodes, especially during Asia crisis and subprime mortgage crisis periods. Moreover, the distinct role of each market is also investigated.     

Learning and time-varying macroeconomic volatility

This paper presents a DSGE model in which agents׳ learning about the economy can endogenously generate time-varying macroeconomic volatility. Economic agents use simple models to form expectations and need to learn the relevant parameters. Their gain coefficient is endogenous and is adjusted according to past forecast errors.The model is estimated using likelihood-based Bayesian methods. The endogenous gain is jointly estimated with the structural parameters of the system.The estimation results show that private agents appear to have often switched to constant-gain learning, with a high constant gain, during most of the 1970s and until the early 1980s, while reverting to a decreasing gain later on. As a result, the model can generate a pattern of volatility, which is increasing in the 1970s and falling in the second half of the sample, with a decline that can roughly match the magnitude of the so-called “Great Moderation” in the 1984–2007 period. The paper also documents how a failure to incorporate learning into the estimation may lead econometricians to spuriously find time-varying volatility in the exogenous shocks, even when these have constant variance by construction.     

Modeling dynamic conditional correlations with leverage effects and volatility spillover effects: Evidence from the Chinese and US stock markets affected by the recent trade friction

In this article, we investigate the dynamic conditional correlations (DCCs) with leverage effects and volatility spillover effects that consider time difference and long memory of returns, between the Chinese and US stock markets, in the Sino-US trade friction and previous stable periods. The widespread belief that the developed markets dominate the emerging markets in stock market interactions is challenged by our findings that both the mean and volatility spillovers are bidirectional. We do find that most of the shocks to these DCCs between the two stock markets are symmetric, and all the symmetric shocks to these DCCs are highly persistent between Shanghai’s trading return and S&P 500′s trading or overnight return, however all the shocks to these DCCs are short-lived between S&P 500′s trading return and Shanghai’s trading or overnight return. We also find clear evidence that the DCC between Shanghai’s trading return and S&P 500′s overnight return has a downward trend with a structural break, perhaps due to the “America First” policy, after which it rebounds and fluctuates sharply in the middle and later periods of trade friction. These findings have important implications for investors to pursue profits.