Realized Volatility Model Research Articles

Asymmetric effect of trading volume on realized volatility

This study examines the asymmetric effect of trading volume on realized volatility and introduces two new realized volatility models to examine this effect: one model uses asymmetric trading volume variables based on intraday returns, while the other uses asymmetric trading volume variables based on daily returns. These new variables are introduced into the heterogeneous autoregressive models with the leverage effect and realized semivariance. The in-sample estimation results show that the asymmetric trading volume variables are clearly significant. Furthermore, out-of-sample forecasting comparisons indicate that asymmetric trading volume variables increase the forecasting performance of realized volatility. These empirical analyses demonstrate that considering asymmetric trading volume in modeling and forecasting realized volatility is important. This study’s findings provide valuable information for understanding and controlling asset and market risks.

Application of Copula Methods in Financial Risk Management: Case of the Zimbabwe Stock Exchange and the Victoria Falls Stock Exchange.

In order to minimize risks and create a safe investing environment, financial risk management is becoming more and more crucial for individuals, financial organizations, and even entire nations. Accurately assessing financial risks and using that information to inform wise investment choices can give an investor a competitive edge as well as significant returns. In actuality, real-world financial variables limit the ability to estimate financial risks. On the other hand, a wealth of data indicates that financial variables typically have asymmetric dependency, skewness, and fat tails. In three ways, the conventional approaches to financial risk management based on normally distributed hypotheses are put to the test by these stylized characteristics of financial variables. First, the univariate normal distribution or other elliptical distributions are unable to adequately fit the distribution of the univariate variable. Second, despite their straightforward tractability, multivariate variables’ extra kurtosis and skewness are not captured by their normal distribution. As a result, the dependence risks associated with multivariate financial variables may be underestimated. Finally, when the joint distribution of various variables is non-elliptical, linear correlation which is typically employed to characterize the dependence of various variables in traditional portfolio risk management is likewise insufficient. This research uses a promising technique based on copulas in conjunction with GARCH and realized volatility models to examine the risks associated with multivariate financial variables in order to address these issues. The multivariate distributions are constructed using copulas in conjunction with GARCH and Realized Volatility models which are then utilized to evaluate portfolio risks in financial market. The findings demonstrate that copula-based models outperform conventional models in fitting financial data. Second, a variety of marginal models have a notable impact on the value at risk of the portfolio, including the GARCH and realized volatility models. Lastly, both the dependence structure and the marginal distribution exhibit notable skewness. Consequently, compared to the normal or Student-t distribution, the skewed Student-t distribution fits some datasets better.

High-frequency enhanced VaR: A robust univariate realized volatility model for diverse portfolios and market conditions.

In the field of financial risk management, the accuracy of portfolio Value-at-Risk (VaR) forecasts is of critical importance to both practitioners and academics. This study pioneers a comprehensive evaluation of a univariate model that leverages high-frequency intraday data to improve portfolio VaR forecasts, providing a novel contrast to both univariate and multivariate models based on daily data. Existing research has used such high-frequency-based univariate models for index portfolios, it has not adequately studied their robustness for portfolios with diverse risk profiles, particularly under changing market conditions, such as during crises. Our research fills this gap by proposing a refined univariate long-memory realized volatility model that incorporates realized variance and covariance metrics, eliminating the necessity for a parametric covariance matrix. This model captures the long-run dependencies inherent in the volatility process and provides a flexible alternative that can be paired with appropriate return innovation distributions for VaR estimation. Empirical analyses show that our methodology significantly outperforms traditional univariate and multivariate Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) models in terms of forecasting accuracy while maintaining computational simplicity and ease of implementation. In particular, the inclusion of high-frequency data in univariate volatility models not only improves forecasting accuracy but also streamlines the complexity of portfolio risk assessment. This research extends the discourse between academic research and financial practice, highlighting the transformative impact of high-frequency data on risk management strategies within the financial sector.

On the relevance of realized quarticity for exchange rate volatility forecasts

<p>High-frequency tick data have proved helpful for forecasting volatility across asset classes. In the finite samples typically faced by practitioners, however, noise inherent in tick-level prices creates inaccuracies in model parameter estimates and resulting forecasts. A remedy proposed to alleviate these measurement errors is to include higher-order moments, more specifically the realized quarticity, in volatility prediction models. In this paper, we investigate the relevance of this approach in foreign exchange markets, as represented by EURUSD and USDJPY data from 2010 to 2022. Using well-established realized volatility models, we find that including realized quarticity leads to higher precision in daily, weekly, and monthly out-of-sample forecasts. These results are robust across estimation windows, evaluation metrics, and model specifications.</p>

Business applications and state‐level stock market realized volatility: A forecasting experiment

AbstractWe analyze the predictive value of (the surprise component of) state‐level business applications, as a proxy of local investor sentiment, for the state‐level realized US stock‐market volatility. We use high‐frequency data for the period from September 2011 to October 2021 to compute realized volatility. Using an extended version of the popular heterogeneous autoregressive realized volatility model and accounting for the possibility that users of forecasts have an asymmetric loss function, we show that business applications tend to have predictive value for realized state‐level stock‐market volatility, as well as for upside (“good”) and downside (“bad”) realized volatility, for users of forecasts who suffer a larger loss from an underprediction of realized volatility than from an overprediction of the same (absolute) seize, after controlling for realized moments (realized skewness, realized kurtosis, realized jumps, and realized tail risks). We also highlight that the COVID‐19 period is a major driver of our empirical results.

Forecasting the volatility of crude oil futures: A time‐dependent weighted least squares with regularization constraint

AbstractParameter instability and model uncertainty are two key problems affecting forecasting outcomes. In this paper, we propose a time‐dependent weighted least squares with ridge constraint (TWLS‐Ridge) to solve the above two problems in the forecasting procedure. The new TWLS‐Ridge approach is applied to the heterogenous autoregressive realized volatility model and its various extensions. The empirical results suggest that TWLS‐Ridge produces more accurate volatility forecasts than several alternative models dealing with parameter instability and model uncertainty. The superior performance of TWLS‐Ridge is robust under different forecast horizons, evaluation periods, and loss functions. An investor with mean–variance preference can improve utility using TWLS‐Ridge forecasts of oil volatility instead of ordinary least squares model forecasts.

Evaluating the performance of futures hedging using factors-driven realized volatility

The complexity and uncertainty of the financial market mainly stem from the rich market internal transaction information and a wide range effect of external factors. To this end, this paper proposes the combination factors-driven forecasting method to predict realized volatilities of the CSI 300 index and index futures. Based on the volatilities predicted by the proposed method, we further evaluate the ex-ante hedging performance in comparison to the conventional HAR model as well as GARCH-type models. The empirical results indicate that the factors-driven realized volatility model significantly dominates the other commonly used models in terms of hedging effectiveness. Furthermore, the superiority of the proposed method is robust in different market conditions, including significant rising or falling and abnormal market fluctuations in the COVID-19 pandemic, and in different index markets. Therefore, this paper improves the prediction accuracy of volatility by integrating market internal transaction information and external factor information, and the proposed method in this paper can be used by investors to obtain an excellent hedging effect.

Measurement of Economic Fluctuations Based on High-Frequency Financial Time Series

In order to improve the analysis and forecasting effect of economic fluctuations, this paper combines the high-frequency financial sequence algorithm to conduct measured analysis of economic fluctuations. Under the continuous jump-diffusion price model, this paper considers the jump part and the continuous part in the process of asset pricing. Moreover, for the jump part, this paper uses the wavelet method to analyze the observation data, and obtains the estimator of the second-order jump covariation difference matrix and its convergence speed. For the continuous part, this paper adopts a two-scale realized volatility model under the continuous price model. In addition, this paper verifies the effect of the intelligent model proposed in this paper through simulation experiments. The simulation data shows that the economic fluctuation analysis system based on high-frequency financial time series proposed in this paper has good economic analysis and economic forecasting effects.

Research on Parameter Estimation and Prediction of Sports Financial Market Volatility Model

At present, the utility function of the financial system in the sports industry has not been brought into full play. Volatility reflects the uncertainty of asset price changes and plays an important role in asset pricing, portfolio, risk management, and asset allocation. Volatility has the characteristics of thick tail, leverage, market linkage, long memory, and aggregation. There are differences between different markets and countries. Therefore, according to the complex characteristics of volatility, this paper uses the feature-oriented research method to study several volatility prediction models, namely, random volatility model, realized volatility model, and multivariate volatility model. In order to promote capital formation and alleviate the financing constraints of sports finance, it provides reference value for reducing transaction costs, improving the quality and efficiency of sports industry, and realizing sustainable and rapid development.

Unrestricted maximum likelihood estimation of multivariate realized volatility models

The popular conditional autoregressive Wishart (CAW) model for dynamics of realized covariance matrices provides a flexible parametrisation. However, the number of parameters grows quadratically with the number of assets, which causes enormous computational difficulties in higher dimensions. Therefore, its unrestricted maximum likelihood (ML) estimation up to now has been conducted only for small portfolios with around five assets. In this paper we elaborate on unrestricted ML estimation of the CAW model in higher dimensions for around 30 assets which is a sufficient number for portfolio diversification. We do so by providing various explicit analytical results for computing the gradient for log-likelihood optimization.

Modeling and Forecasting the Realized Volatility of Bitcoin using Realized HAR-GARCH-type Models with Jumps and Inverse Leverage Effect

Using the high-frequency data of Bitcoin, this study aims to model the time-varying volatility identified in the residuals of the heterogeneous autoregressive (HAR) model of realized volatility using the symmetric, asymmetric and long-memory generalized autoregressive conditional heteroscedastic models (GARCH) models. We further extended these models by incorporating jumps and continuous components in the realized volatility estimators and investigating the impact of the inverse leverage effect. The Diebold Mariano and model confidence set test confirm that the forecasting performance of HAR-type models can be effectively improved by these innovations. The long memory HAR-GARCH model with jumps and continuous components provided better forecasting accuracy for Bitcoin volatility as compared to other realized volatility models. The findings of this study may benefit individual investors and risk managers who wish to minimize risks and diversify their portfolios to maximize profits in Bitcoin’s investment.

Realizing correlations across asset classes

We introduce a simple and intuitive composite model for forecasting correlations for use in portfolio optimization. Each element of the composite model is based on a realized volatility model. To test our model, we consider an investor seeking to diversify an equity portfolio by including commodities. In a high-frequency setting, we demonstrate that significant economic gains can be achieved by basing portfolio decisions on our modeling framework. The gains depend on the quality of the chosen volatility model, and for our preferred model, they are economically significant despite the realistic constraints on short selling and portfolio turnover.

Empirical Research on the Prediction Effect of Volatility Model Based on the Perspective of Investor Sentiment Health and Market Liquidity.

Healthy investor sentiment has an important impact on stock market volatility. To avoid extreme volatility in the stock market, it becomes crucial to focus on the sentiment health of investors. Therefore, we establish the realized volatility model, the implied volatility model, and the historical volatility model, respectively, introduce investor sentiment and market liquidity into these models, and empirically study the forecast effects of future daily and weekly frequency volatility to play a role in the development of the physical industry and the improvement of organizational performance. The study found that the HAR-RV model has the strongest predictive ability, while the GJR-GARCH model's predictive effect is not ideal; market liquidity and high investor sentiment can improve the predictive effect of most models; compared with long-term (one-week) volatility, the effect of predicting short-term (one-day) volatility is better.

Increasing the information content of realized volatility forecasts

Abstract 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.

Forecasting volatility using double shrinkage methods

In this paper, we propose and evaluate a shrinkage based methodology that is designed to improve the accuracy of volatility forecasts. Our approach is based on a two-step procedure for extracting latent common volatility factors from a large dimensional and high-frequency dataset. In the first step, we apply either least absolute shrinkage operator (LASSO) or the elastic net (EN) shrinkage on estimated integrated volatilities, in order to select a subset of assets that are informative about the target asset. In the second step, we utilize (sparse) principal component analysis on the selected assets, in order to estimate latent return factors, which are in turn used to construct latent volatility factors. Our two-step method is found to yield more accurate volatility predictions than a variety of alternative models based on approaches such as direct application of (S)PCA and direct application of LASSO or EN shrinkage, when comparing out-of-sample R2s and mean absolute forecasting errors, and when implementing predictive accuracy tests. Additionally model confidence sets are found to contain models solely based on our two-step approach. These forecasting gains are found to be robust to the use of original or log-scale realized volatility models, different data sampling frequencies, and different forecasting sub-periods.

Can night trading sessions improve forecasting performance of gold futures' volatility in China?

AbstractWe use heterogeneous autoregression (HAR) and two related HAR extension models to examine volatility forecasting performances before and after the launch of night trading sessions in the Shanghai Futures Exchange (SHFE) gold futures market. To capture fluctuations from external information and volatility of realized volatility (RV), we incorporate the trading volume and jumping into the HAR‐V‐J model in the first place and then incorporate a GARCH specification into the HAR‐GARCH model. Results showed that there were large fluctuations in SHFE gold futures market before the launch of night trading sessions and mostly stemmed from overnight fluctuation in the international gold futures market. After the launch of night trading sessions, the realized volatility has a clear trend of moderation. In the in‐sample estimation, both jump and external information are found to have significant explanatory power with the HAR‐V‐J model. Additionally, the volatility clustering and high persistence of the realized volatility were confirmed by the GARCH coefficients. Last but not the least, night trading sessions have significantly improved the out‐of‐sample forecasting performances of realized volatility models. Among them, the HAR‐V‐J model is the best‐performing model. This conclusion holds for various prediction horizons and has great practical values for investors and policymakers.

Forecasting the oil price realized volatility: A multivariate heterogeneous autoregressive model

AbstractIn this study, we investigate the impacts of common information between oil futures and the United States stock markets on forecasting oil volatility using the multivariate heterogeneous autoregressive realized volatility model. We have several noteworthy findings. First, the in‐sample estimation results show that the negative returns and the ‘bad’ jumps have larger influence on oil futures volatility than positive returns and ‘good’ jumps, respectively. Second, the out‐of‐sample results further indicate that our multivariate heterogeneous autoregressive (HAR) model can generate higher forecast accuracy than individual HAR model for the realized volatility‐type models, which highlights the importance of incorporating volatility information from the stock Market. Third, our findings are robust across the direction‐of‐change test and different windows. Furthermore, from the perspective of the investors' allocation portfolio in the future, the use of common information can also bring greater gains.

Predicting risk in energy markets: Low-frequency data still matter

Are high-frequency data always needed to generate precise forecasts of risk measures in energy markets? This study attempts to shed light on this question. We study whether energy market participants can rely on low-frequency volatility estimators when interested in two market risks: volatility and expected shortfall. Using ten years of data on four of the world’s most liquid energy futures contracts – the crude oil benchmarks West Texas Intermediate and Brent, as well as natural gas and heating oil futures – we provide conclusive evidence that while realized volatility models lead to much more accurate forecasts in the short term, medium- and longer-term forecasts based on daily ranges are comparable and, in some cases, even more accurate than their high-frequency counterparts that are computationally more intensive and that require costly data. Next, we present an application to predict extreme price declines - expected shortfall - with low-frequency volatility estimates. For that purpose, we propose a novel complete subset quantile regression model to predict multiple-day-ahead expected shortfall . Our back-testing results show that the new model leads to well-specified price decline forecasts, particularly when used with low-frequency volatility estimates. These results show that depending on the forecast horizon and purpose, low-frequency, publicly available, free of cost and easy to process volatility estimators still matter.

A DCC-type approach for realized covariance modeling with score-driven dynamics

We propose a class of score-driven realized covariance models where volatilities and correlations are separately estimated. We can thus combine univariate realized volatility models with a recently introduced class of score-driven realized covariance models based on Wishart and matrix-F distributions. Compared to the latter, the proposed models remain computationally simple at high dimensions and allow for higher flexibility in parameter estimation. Through a Monte-Carlo study, we show that the two-step maximum likelihood procedure provides accurate parameter estimates in small samples. Empirically, we find that the proposed models outperform those based on joint estimation, with forecasting gains that become more significant as the cross-section dimension increases.

VIX futures and its closed‐form pricing through an affine GARCH model with realized variance

AbstractThis paper studies the forecasting of volatility index (VIX) and the pricing of its futures by a generalized affine realized volatility model proposed by Christoffersen et al. This model is a weighted average of a GARCH and a pure realized variance (RV) model that incorporates each volatility component into the new dynamics. We rewrite the VIX in terms of both volatility components and then derive closed‐form formulas for the VIX forecasting and its futures pricing. Our empirical studies find that a unification of the GARCH and the RV in the modeling substantially improves the forecasting of this index and the pricing of its futures.