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This study explores the risk of the traditional momentum strategy in terms of its realized variance using various data frequencies. It is shown that momentum risk is infinite regardless of the data frequency, implying that (a) t-statistics for this strategy do not exist, (b) correlation-based metrics such as Sharpe ratios do not exist either, and (c) the momentum premium is not observable in reality. It is further shown that the time-honored lognormal distribution is unable to accurately model extreme events observed at various variance data frequencies. Finally, it is shown that the well-known effect of time aggregation does not work for this investment vehicle. Hence, the study is forced to conclude that momentum stories have no valid foundation for their claims. [ABSTRACT FROM AUTHOR]

This paper investigates the high‐frequency volatility modeling and prediction for crude oil futures in China, a new asset class emerging in recent years. Two volatility measures, the realized variance (RV) and realized bi‐power variations (RBV) are constructed at various frequencies by virtue of 1‐minute crude oil futures prices. The distinctive components of these volatility estimators are further identified to exploit the information contents in the in‐sample explanatory power of the realized variance dynamics and the out‐of‐sample prediction of realized variance across different horizons, leading to four new HAR‐RV‐type models. First, the empirical results show that the continuous component of the weekly realized variance, representing investors' trading behavior in the medium‐term, is the dominant factor driving up volatility trends in China's crude oil futures market over a range of market conditions. Second, the monthly jump component in realized variance presents the significant in‐sample explanatory power, and yet marginally improves prediction performance in realized variance during the two out‐of‐sample periods. Finally, these results are robust toward various market/model setups, over day‐ and night‐trading hours, and across a range of prediction horizons and relative to prediction benchmarks. [ABSTRACT FROM AUTHOR]

In this study, we propose a dynamic partial (co)variance forecasting model (DPCFM) by introducing a dynamic model averaging (DMA) approach into a partial (co)variance forecasting model. The dynamic partial (co)variance forecasting model considers the time-varying property of the model's parameters and optimal threshold combinations used to construct partial (co)variance. Our empirical results suggest that in both variance and covariance cases, the dynamic partial variance forecasting model can generate more accurate forecasts than an individual partial (co)variance forecasting model in both the statistical and economic sense. The superiority of the dynamic partial (co)variance forecasting model is robust to various forecast horizons. [ABSTRACT FROM AUTHOR]

This article contributes to our understanding of the macro‐financial linkages in the high‐frequency domain during the recent health crisis. Building on the extant literature that mainly uses monthly or quarterly macro proxies, we examine the daily economic impact on intra‐daily financial volatility by applying the macro‐augmented HEAVY model with asymmetries and power transformations. Our study associates US and UK financial with macroeconomic uncertainties in addition to further macro drivers that exacerbate equity market volatility. Daily local economic policy uncertainty is one of the main drivers of financial volatility, alongside global credit and commodity factors. Higher macro uncertainty is found to increase the leverage and macro effects from credit and commodity markets on US and UK stock market realized volatility. Most interestingly, the Covid‐19 outbreak is found to exert a considerable impact on financial volatilities through the uncertainty channel, given the prevalent worry about controversial policy interventions to support societies and markets, particularly in the case of the severely censured US and UK governments' reluctant and limited response in the very beginning of the pandemic. [ABSTRACT FROM AUTHOR]

We show that the realized GARCH model yields closed-form expression for both the volatility index (VIX) and the volatility risk premium (VRP). The realized GARCH model is driven by two shocks, a return shock and a volatility shock, and these are natural state variables in the stochastic discount factor (SDF). The volatility shock endows the exponentially affine SDF with compensation for volatility risk. This leads to dissimilar dynamic properties under the physical and risk-neutral measures that can explain time-variation in the VRP. In an empirical application with the S&P 500 returns, the VIX, and the VRP, we find that the realized GARCH model significantly outperforms conventional GARCH models. [ABSTRACT FROM AUTHOR]

This is a personal assessment of the intellectual contribution of the Black–Scholes model of option pricing. I argue that the real contribution of the paper is to show that European options can be replicated exactly if the future variability of the path of transaction prices is known. The continuous rebalancing and the probabilistic setting of the original paper mask this insight. [ABSTRACT FROM AUTHOR]

We inspect how accurate machine learning (ML) is at forecasting realized variance of the Dow Jones Industrial Average index constituents. We compare several ML algorithms, including regularization, regression trees, and neural networks, to multiple heterogeneous autoregressive (HAR) models. ML is implemented with minimal hyperparameter tuning. In spite of this, ML is competitive and beats the HAR lineage, even when the only predictors are the daily, weekly, and monthly lags of realized variance. The forecast gains are more pronounced at longer horizons. We attribute this to higher persistence in the ML models, which helps to approximate the long memory of realized variance. ML also excels at locating incremental information about future volatility from additional predictors. Lastly, we propose an ML measure of variable importance based on accumulated local effects. This shows that while there is agreement about the most important predictors, there is disagreement on their ranking, helping to reconcile our results. [ABSTRACT FROM AUTHOR]

Assuming N available calendar days, each with M intraday returns, the realized volatility literature suggests creating N end-of-day estimators by summing the M squared returns from each particular date. Instead of this "Calendar" [realized variance (RV)] approach, we propose a "Rolling" [rolling RV (RRV)] approach that simply sums trailing M returns at each timestamp, regardless if all M returns belong to the same calendar date. When estimating an out-of-sample 1-day realized volatility model, the former results in an ordinary least squares (OLS) regression with N− 1 datapoints while the latter incorporates M (N − 2) + 1 datapoints, effectively lowering the standard errors, and potentially resulting in more accurate forecasts. We compare both models for the S&P 500 and 26 Dow Jones Industrial Average stocks; our results generally suggest that the Rolling approach yields both statistically and economically significant superior out-of-sample performance over the traditional Calendar approach. [ABSTRACT FROM AUTHOR]

In this paper, we develop a penalized realized variance (PRV) estimator of the quadratic variation (QV) of a high-dimensional continuous Itô semimartingale. We adapt the principle idea of regularization from linear regression to covariance estimation in a continuous-time high-frequency setting. We show that under a nuclear norm penalization, the PRV is computed by soft-thresholding the eigenvalues of realized variance (RV). It therefore encourages sparsity of singular values or, equivalently, low rank of the solution. We prove our estimator is minimax optimal up to a logarithmic factor. We derive a concentration inequality, which reveals that the rank of PRV is—with a high probability—the number of non-negligible eigenvalues of the QV. Moreover, we also provide the associated non-asymptotic analysis for the spot variance. We suggest an intuitive data-driven subsampling procedure to select the shrinkage parameter. Our theory is supplemented by a simulation study and an empirical application. The PRV detects about three–five factors in the equity market, with a notable rank decrease during times of distress in financial markets. This is consistent with most standard asset pricing models, where a limited amount of systematic factors driving the cross-section of stock returns are perturbed by idiosyncratic errors, rendering the QV—and also RV—of full rank. [ABSTRACT FROM AUTHOR]

We examine the predictive value of El Niño and La Niña weather episodes for the subsequent realized variance of 16 agricultural commodity prices. To this end, we use high‐frequency data covering the period from 2009 to 2020 to estimate the realized variance along realized skewness, realized kurtosis, realized jumps, and realized upside and downside tail risks as control variables. Accounting for the impact of the control variables as well as spillover effects from the realized variances of the other agricultural commodities in our sample, we estimate an extended heterogeneous autoregressive (HAR) model by means of random forests to capture in a purely data‐driven way potentially nonlinear links between El Niño and La Niña and the subsequent realized variance. We document such nonlinear links, and that El Niño and La Niña increase forecast accuracy, especially at longer forecast horizons, for several of the agricultural commodities that we study in this research. [ABSTRACT FROM AUTHOR]

This paper proposes a model for realized variance that exploits information in realized quarticity. The realized variance and quarticity measures are both highly persistent and highly correlated with each other. The proposed model incorporates information from the observed realized quarticity process via autoregressive conditional variance dynamics. It exploits conditional dependence in higher order (fourth) moments in analogy to the class of GARCH models exploit conditional dependence in second moments.

This paper extends the Realized-GARCH framework, by allowing the conditional variance equation to incorporate exogenous variables related to intra-day realized measures. The choice of these measures is motivated by the so-called heterogeneous auto-regressive (HAR) class of models. Our augmented model is found to outperform both the Realized-GARCH and the various HAR models in terms of in-sample fitting and out-of-sample forecasting accuracy. The new model specification is examined under alternative parametric density assumptions for the return innovations. Non-normality seems to be very important for filtering the return innovations to which variance responds and helps significantly upon the prediction performance of the suggested model. [ABSTRACT FROM AUTHOR]

Abstract This study investigates the predictability of a fixed uncertainty index (UI) for realized variances (volatility) in the international stock markets from a high-frequency perspective. We construct a composite UI based on the scaled principal component analysis (s-PCA) method and demonstrate that it exhibits significant in- and out-of-sample predictabilities for realized variances in global stock markets. This predictive power is more powerful than those of two commonly employed competing methods, namely, PCA and the partial least squares (PLS) methods. The result is robust in several checks. Further, we explain that s-PCA outperforms other dimension-reduction methods since it can effectively increase the impacts of strong predictors and decrease those of weak factors. The implications of this research are significant for investors who allocate assets globally.

Simulations and empirical studies suggest that incorporating a discontinuous jump process in asset pricing models improve volatility forecasting, pricing of instruments, and hedging positions in a portfolio. In this paper we analyze high frequency market data of Colombian sovereign bonds to study the presence or absence of discontinuities in the price generating process. We find that Colombian sovereign debt experiments jumps across all maturities but with different frequencies, in particular, we do not find that long term bonds jump less frequently than short term bonds. Furthermore, bonds with closer maturities cojump in greater magnitude than those with a greater distance between them. Finally, we find significant day-of-the-week effects, as well as an important increase in the jump frequency due to surprises in economic information related to US monetary policy, and no effect due to direct monetary policy announcements in Colombia. [ABSTRACT FROM AUTHOR]

This paper considers the use of multiple noisy daily realized variance measures to extract a denoised latent variance process. The class of stochastic volatility models used for signal extraction has the important feature that they can be written as a linear state space model. As a result, prediction of the denoised latent variance and likelihood evaluation can be carried out efficiently using the Kalman filter. This is in contrast to stochastic models that jointly model the return and variance, which require computationally expensive nonlinear filtering for prediction and inference. The gain from using multiple noisy daily variance measures is examined empirically for the S&P 500 index using daily OHLC (open-high-low-close) data. [ABSTRACT FROM AUTHOR]

We develop a statistical theory for a continuous time approximately log‐normal fractional stochastic volatility model to examine whether the volatility is rough, that is, whether the Hurst parameter is less than one half. We construct a quasi‐likelihood estimator and apply it to realized volatility time series. Our quasi‐likelihood is based on the error distribution of the realized volatility and a Whittle‐type approximation to the auto‐covariance of the log‐volatility process. We prove the consistency of our estimator under high‐frequency asymptotics, and examine by simulations its finite sample performance. Our empirical study suggests that the volatility of the time series examined is indeed rough. [ABSTRACT FROM AUTHOR]

This paper proposes a model for realized variance that exploits information in realized quarticity. The realized variance and quarticity measures are both highly persistent and highly correlated with each other. The proposed model incorporates information from the observed realized quarticity process via autoregressive conditional variance dynamics. It exploits conditional dependence in higher order (fourth) moments in analogy to the class of GARCH models exploit conditional dependence in second moments. [ABSTRACT FROM AUTHOR]

We examine the forecasting power of a daily newspaper‐based index of uncertainty associated with infectious diseases (EMVID) for real estate investment trusts (REITs) realized market variance of the United States (US) via the heterogeneous autoregressive realized volatility (HAR‐RV) model. Our results show that the EMVID index improves the forecast accuracy of realized variance of REITs at short‐, medium‐, and long‐run horizons in a statistically significant manner, with the result being robust to the inclusion of additional controls (leverage, realized jumps, skewness, and kurtosis) capturing extreme market movements, and also carries over to 10 sub‐sectors of the US REITs market. Our results have important portfolio implications for investors during the current period of unprecedented levels of uncertainty resulting from the outbreak of COVID‐19. [ABSTRACT FROM AUTHOR]

The research debate on the informational content embedded in option prices mostly approves the incremental predictive power of implied volatility estimates for financial volatility forecasting beyond that contained in GARCH and realized variance models. Contributing to this ongoing debate, we introduce the novel AIM-HEAVY model, a tetravariate system with asymmetries, option-implied volatility, and economic uncertainty variables beyond daily and intra-daily dispersion measures included in the benchmark HEAVY specification. We associate financial with macroeconomic uncertainties to explore the macro-financial linkages in the high-frequency domain. In this vein, we further focus on economic factors that exacerbate stock market volatility and represent major threats to financial stability. Hence, our findings are directly connected to the current world-wide Coronavirus outbreak. Financial volatilities are already close to their crisis-peaks amid the generalized fear about controversial economic policies to support societies and the financial system, especially in the case of the heavily criticized UK authorities' delayed and limited response. [ABSTRACT FROM AUTHOR]

Abstract In this work we study how company co-occurrence in news events can be used to discover business links between them. We develop a methodology that is able to process raw textual data, embed it into a numerical form, and extract a meaningful network of connections. Each news event is considered as a node on the graph and we define the similarity between the two events as the cosine similarity between their vectors in the embedded space. Using this procedure, we contribute to the literature by successfully reconstructing business links between companies, which is usually a difficult task since the data on this topic is either outdated, incomplete or not widely available. We then demonstrate possible uses of this network in two forecasting applications. First, we show how the network can be used as an exogenous feature vector, which improves the prediction of the correlation between companies in the network. This correlation is determined from their realized variance as well as using a wide set of machine learning models for prediction. Second, we demonstrate the use of network for predicting future events with point processes. Our methodology can be applied on any series of events, where we have demonstrated and evaluated its applicability on news events and large market moves. For most of the tested algorithms the experimental results show an improvement in performance when including information from our graphs. More specifically, in certain sectors using Neural Networks shows improved performance by up to 50%.

We contribute to the empirical literature on the predictability of oil-market volatility by comparing the predictive role of aggregate versus several disaggregated metrics of policy-related and equity-market uncertainties of the USA and geopolitical risks for forecasting the future realized volatility of oil-price (WTI) returns over the monthly period from 1985:01 to 2021:08. Using machine-learning techniques, we find that adding the disaggregated metrics to the array of predictors improves the accuracy of forecasts at intermediate and long forecast horizons, and mainly when we use random forests to estimate our forecasting model. [ABSTRACT FROM AUTHOR]

This paper studies the US and global economic fundamentals that exacerbate emerging stock markets volatility and can be considered as systemic risk factors increasing financial stability vulnerabilities. We apply the bivariate HEAVY system of daily and intra-daily volatility equations enriched with powers, leverage, and macro-effects that improve its forecasting accuracy significantly. Our macro-augmented asymmetric power HEAVY model estimates the inflammatory effect of US uncertainty and infectious disease news impact on equities alongside global credit and commodity factors on emerging stock index realized volatility. Our study further demonstrates the power of the economic uncertainty channel, showing that higher US policy uncertainty levels increase the leverage effects and the impact from the common macro-financial proxies on emerging markets' financial volatility. Lastly, we provide evidence on the crucial role of both financial and health crisis events (the 2008 global financial turmoil and the recent Covid-19 pandemic) in raising markets' turbulence and amplifying the volatility macro-drivers impact, as well. [ABSTRACT FROM AUTHOR]

This study investigates the predictability of a fixed uncertainty index (UI) for realized variances (volatility) in the international stock markets from a high-frequency perspective. We construct a composite UI based on the scaled principal component analysis (s-PCA) method and demonstrate that it exhibits significant in- and out-of-sample predictabilities for realized variances in global stock markets. This predictive power is more powerful than those of two commonly employed competing methods, namely, PCA and the partial least squares (PLS) methods. The result is robust in several checks. Further, we explain that s-PCA outperforms other dimension-reduction methods since it can effectively increase the impacts of strong predictors and decrease those of weak factors. The implications of this research are significant for investors who allocate assets globally. [ABSTRACT FROM AUTHOR]

Using a large dataset on major FX rates, we test the robustness of the rough fractional volatility model over different time scales, by including smoothing and measurement errors into the analysis. Our findings lead to new stylized facts in the log–log plots of the second moments of realized variance increments against lag which exhibit some convexity in addition to the roughness and stationarity of the volatility. The very low perceived Hurst exponents at small scales are consistent with the rough framework, while the higher perceived Hurst exponents for larger scales lead to a nonlinear behaviour of the log–log plot that has not been described by models introduced so far. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the problem of pricing discretely sampled variance swaps under a hybrid stochastic model. Our modeling framework is a combination with a double Heston stochastic volatility model and a Cox–Ingersoll–Ross stochastic interest rate process. Due to the application of the T-forward measure with the stochastic interest process, we can only obtain an efficient semi-closed form of pricing formula for variance swaps instead of a closed-form solution based on the derivation of characteristic functions. The practicality of this hybrid model is demonstrated by numerical simulations. [ABSTRACT FROM AUTHOR]

This paper specifies a semiparametric variance impulse response function using realized variances. The news impact and impulse responses are estimated using local projection methods using least squares and external instruments. Compared to impulse responses estimated from parametric GARCH type models, semiparametric local projection responses show less persistence though the estimates are quite noisy. [ABSTRACT FROM AUTHOR]

A multivariate GARCH model of natural resources is specified to capture the effects of time varying portfolio risk. A special feature of the model is the inclusion of realized volatility for natural resource assets that are available at multiple frequencies as well as being sensitive to sudden changes in climatic conditions. Natural resource portfolios under climate change are simulated from bootstrapping schemes as well as being derived from global climate model projections. Both approaches are applied to a multiasset water portfolio model consisting of reservoir inflows, rainwater harvesting, and desalinated water. The empirical results show that while reservoirs remain the dominant water asset, adaptation to climate change involves increased contributions from rainwater harvesting and more frequent use of desalinated water. It is estimated that climate change increases annual water supply costs by between 7% and 44% over a 20‐year forecast horizon. [ABSTRACT FROM AUTHOR]

This paper studies the bivariate HEAVY system of volatility regression equations and its various extensions that are directly applicable to the day-to-day business treasury operations of trading in foreign exchange and commodities, investing in bond and stock markets, hedging out market risk, and capital budgeting. We enrich the HEAVY framework with powers, asymmetries, and long memory that improve its forecasting accuracy significantly. Other findings are as follows. First, hyperbolic memory fits the realized measure better, whereas fractional integration is more suitable for the powered returns. Second, the structural breaks applied to the bivariate system capture the time-varying behavior of the parameters, in particular during and after the global financial crisis of 2007/2008. [ABSTRACT FROM AUTHOR]

This paper evaluates the information content in daily volatility measures that utilize OHLC (Open‐High‐Low‐Close) price data. An encompassing regression framework is used to evaluate the absolute and relative information contain in such measures. 2‐step GMM (generalized method of moments) estimates using two sets of instruments are used to address potential bias from measurement errors. The evidence using S&P 500 index data suggest that volatility measures that use OHLC data encompass those based only on close‐to‐close returns or high‐minus‐low ranges. However, the proposed instruments do not all pass statistical tests of instrument validity and the identification robust confidence set can be quite large. [ABSTRACT FROM AUTHOR]

Background: Since high-frequency data have become available, an unbiased volatility estimator, i.e. realized variance (RV) can be computed. Commonly used models for RV forecasting suffer from strong persistence with a high sensitivity to the returns distribution assumption and they use only daily returns. Objectives: The main objective is measurement and forecasting of RV. Two approaches are compared: Heterogeneous AutoRegressive model (HAR-RV) and Feedforward Neural Networks (FNNs). Even though HAR-RV-type models describe RV stylized facts very well, they ignore its nonlinear behaviour. Therefore, FNN-HAR-type models are developed. Methods/Approach: Firstly, an optimal sampling frequency with application to the DAX index is chosen. Secondly, in and out of sample predictions within HAR models and FNNs are compared using RMSE, AIC, the Wald test and the DM test. Weights of FNN-HAR-type models are estimated using the BP algorithm. Results: The optimal sampling frequency of RV is 10 minutes. Within HAR-type models, HAR-RV-J has better, but not significant, forecasting performances, while FNN-HAR-J and FNNLHAR- J have significantly better predictive accuracy in comparison to the FNN-HAR model. Conclusions: Compared to the traditional ones, FNN-HAR-type models are better in capturing nonlinear behaviour of RV. FNN-HAR-type models have better accuracy compared to traditional HAR-type models, but only on the sample data, whereas their out-of-sample predictive accuracy is approximately equal.

The primary purpose of this paper is to investigate whether a novel Markov regime‐switching mixed‐data sampling (MRS‐MIADS) model we design can improve the prediction accuracy of the realized variance (RV) of Bitcoin. Moreover, to verify whether the importance of jumps for RV forecasting changes over time, we extend the standard MIDAS model to characterize two volatility regimes and introduce a jump‐driven time‐varying transition probability between the two regimes. Our results suggest that the proposed novel MRS‐MIDAS model exhibits statistically significant improvement for forecasting the RV of Bitcoin. In addition, we find that jump occurrences significantly increase the persistence of the high‐volatility regime and switch between high‐ and low‐volatility regimes. A wide range of checks confirm the robustness of our results. Finally, the proposed model shows significant improvement for 2‐week and 1‐month horizon forecasts. [ABSTRACT FROM AUTHOR]

This study proposes that the overall state of the market, as captured by daily return and volatility, is an important determinant of volatility persistence. By utilizing the realized variance (RV) measure, this paper shows that daily time-varying volatility persistence increases with return but decreases with volatility. Negative returns increase volatility persistence more than positive returns. The dependence of volatility persistence on state variables is termed "conditional volatility persistence". This study finds that conditional volatility persistence is the dominant channel linking changing market states to future volatility and the model which calibrates future-RV conditionally on market states performs better statistically and economically. [ABSTRACT FROM AUTHOR]

This paper studies the bivariate HEAVY system of daily and intra-daily volatility equations and its macro-augmented asymmetric power extension. We focus on economic drivers that exacerbate stock market volatility and can be proved to be major threats for financial stability. Our study proves the inflammatory effects of UK Policy Uncertainty alongside global credit and commodity factors that spread across European financial markets. This UK-led spillover phenomenon should be considered by world market participants and recognized, monitored and mitigated by policymakers amid the Brexit fears and the associated highly probable harm for Europe. Other findings are as follows. First, once we allow for power transformations, asymmetries, and macro-effects in the benchmark specification, it is found that both powered conditional variances are significantly affected by the powers of squared negative returns and realized measure, further improving the HEAVY framework's forecasting accuracy. Second, the structural breaks applied to the bivariate system capture the time-varying behavior of the parameters, in particular during the global financial crisis of 2007/08. Third, higher UK uncertainty levels increase the leverage and global macro-effects from credit and commodity markets on all European stock markets' realized volatilities. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

At present, the study concerning pricing variance swaps under CIR the (Cox–Ingersoll–Ross)–Heston hybrid model has achieved many results; however, due to the instantaneous interest rate and instantaneous volatility in the model following the Feller square root process, only a semi-closed solution can be obtained by solving PDEs. This paper presents a simplified approach to price log-return variance swaps under the CIR–Heston hybrid model. Compared with Cao’s work, an important feature of our approach is that there is no need to solve complex PDEs; a closed-form solution is obtained by applying the martingale theory and Ito^’s lemma. The closed-form solution is significant because it can achieve accurate pricing and no longer takes time to adjust parameters by numerical method. Another significant feature of this paper is that the impact of sampling frequency on pricing formula is analyzed; then the closed-form solution can be extended to an approximate formula. The price curves of the closed-form solution and the approximate solution are presented by numerical simulation. When the sampling frequency is large enough, the two curves almost coincide, which means that our approximate formula is simple and reliable.

We use a dataset for the group of G7 countries and China to study the out-of-sample predictive value of uncertainty and its international spillovers for the realized variance of crude oil (West Texas Intermediate and Brent) over the sample period from 1996Q1 to 2020Q4. Using the Lasso estimator, we found evidence that uncertainty and international spillovers had predictive value for the realized variance at intermediate (two quarters) and long (one year) forecasting horizons in several of the forecasting models that we studied. This result holds also for upside (good) and downside (bad) variance, and irrespective of whether we used a recursive or a rolling estimation window. Our results have important implications for investors and policymakers.

Using data for the group of G7 countries and China for the sample period 1996Q1 to 2020Q4, we study the role of uncertainty and spillovers for the out-of-sample forecasting of the realized variance of gold returns and its upside (good) and downside (bad) counterparts. We go beyond earlier research in that we do not focus exclusively on U.S.-based measures of uncertainty, and in that we account for international spillovers of uncertainty. Our results, based on the Lasso estimator, show that, across the various model configurations that we study, uncertainty has a more systematic effect on out-of-sample forecast accuracy than spillovers. Our results have important implications for investors in terms of, for example, pricing of related derivative securities and the development of portfolio-allocation strategies.

Fully explicit closed-form expressions are developed for the fair strike prices of discrete-time variance swaps under general affine GARCH type models that have been risk-neutralized with a family of variance dependent pricing kernels. The methodology relies on solving differential recursions for the coefficients of the joint cumulant generating function of the log price and the conditional variance processes. An alternative derivation is provided in the case of Gaussian innovations. Using standard assumptions on the asymptotic behavior of the GARCH parameters as the sampling frequency increases, the diffusion limit of a Gaussian GARCH model is derived and the convergence of the variance swap prices to its continuous-time limit is further investigated. Numerical examples on the term structure of the variance swap rates and on the convergence results are also presented. [ABSTRACT FROM AUTHOR]

Change-point time series specifications constitute flexible models that capture unknown structural changes by allowing for switches in the model parameters. Nevertheless most models suffer from an over-parametrization issue since typically only one latent state variable drives the switches in all parameters. This implies that all parameters have to change when a break happens. To gauge whether and where there are structural breaks in realized variance, we introduce the sparse change-point HAR model. The approach controls for model parsimony by limiting the number of parameters which evolve from one regime to another. Sparsity is achieved thanks to employing a nonstandard shrinkage prior distribution. We derive a Gibbs sampler for inferring the parameters of this process. Simulation studies illustrate the excellent performance of the sampler. Relying on this new framework, we study the stability of the HAR model using realized variance series of several major international indices between January 2000 and August 2015. [ABSTRACT FROM AUTHOR]

• A TVC-AHAR model is proposed for forecasting realized variance. • The TVC-AHAR model features asymmetric volatility and time-varying coefficients. • The TVC-AHAR model is easy to implement via maximum likelihood based on Kalman filter. • Empirical results show that the TVC-AHAR model outperforms others in out-of-sample forecasting. This paper proposes an asymmetric HAR model with time-varying coefficients (TVC-AHAR) for modeling and forecasting realized variance. The TVC-AHAR model includes good and bad volatilities and assumes the associated time-varying coefficients to be driven by a latent Gaussian autoregressive process. The model is easy to estimate and implement by using maximum likelihood based on Kalman filter. Empirical analysis using two stock market indices of China, the Shanghai Stock Exchange Composite Index and Shenzhen Stock Exchange Component Index, shows that our proposed TVC-AHAR model yields more accurate out-of-sample forecasts of realized variance compared with the other models. [ABSTRACT FROM AUTHOR]

• We investigate direction and strength of relationships between liquidity and volatility. • Most liquid stocks from the Warsaw Stock Exchange listed in 2006–16 are studied. • We apply tests of Toda-Yamamoto (1995), Hatemi (2012) and Diebold-Yilmaz (2009). • High-low range (liquidity proxy) Granger causes volatility most often. • We find that volatility-liquidity causality is bidirectional; liquidity more often Granger causes volatility than volatility causes liquidity. We study dependencies between liquidity and volatility in the causality framework for stocks listed on the Warsaw Stock Exchange. Using Toda-Yamamoto and Granger causality tests we find bidirectional causality between the measures. The causal liquidity-volatility relation is more often observed than volatility-liquidity one, and both relations are frequently asymmetric. The directional spillover index suggests, that the fraction of forecast error variance due to the shock in other measure is much smaller than the response to own shocks. The choice of proxies matters: among different alternatives we find that high-low range is most often Granger cause for volatility. [ABSTRACT FROM AUTHOR]

We compare forecasts of the volatility of the Australian dollar exchange rate to alternative measures of ex post volatility. We develop and apply a simple test for the improvement in the ability of loss functions to distinguish between forecasts when the quality of a volatility estimator is increased. We find that both realized variance and the daily high–low range provide a significant improvement in loss function convergence relative to squared returns. We find that a model of stochastic volatility provides the best forecasts for models that use daily data, and the GARCH(1,1) model provides the best forecast using high‐frequency data. [ABSTRACT FROM AUTHOR]