ABSTRACT We study the accuracy of a variety of parametric price duration‐based realized variance estimators constructed via various financial duration models and compare their forecasting performance with the performance of various nonparametric return‐based realized variance estimators. Our financial duration models consist of an autoregressive conditional duration (ACD), its logarithmic version (Log–ACD), and the fractionally integrated ACD (FIACD), as well as the Markov switching multifractal duration (MSMD) model and the factorial hidden Markov duration (FHMD) process. In an empirical study using high‐frequency data on 10 stocks traded on the New York stock exchange (NYSE), our in‐sample and out‐of‐sample results show that the parametric price duration‐based realized variance (RV) estimators, especially the ACD‐based RV estimator, seem to be robust to price jumps and microstructure noise and perform better than the non‐parametric return‐based RV estimators. Furthermore, we also find that the price duration‐ and return‐based RV models perform relatively well and produce more accurate and valid value‐at‐risk forecasts than the GARCH(1,1).

This paper introduces a novel discrete-time stochastic volatility model that employs a countably infinite mixture of AR(1) processes, with a Dirichlet process prior, to nonparametrically model the latent volatility. Realized variance (RV) is incorporated as an ex post signal to enhance volatility estimation. The model effectively captures fat tails and asymmetry in both return and log(RV) conditional distributions. Empirical analysis of three major stock indices provides strong evidence supporting the nonparametric stochastic volatility. The results reveal that the volatility equation components exhibit significant variation over time, enabling the estimation of a more dynamic volatility process that better accommodates extreme returns and variance shocks. The new model delivers out-of-sample density forecasts with strong evidence of improvement, particularly for returns, log(RV), and the left region of the return distribution, including negative returns and extreme movements below − 1 % and − 2 % . The new approach provides improvements in forecasting the tail-risk measures of value-at-risk and expected shortfall.

ABSTRACTThis paper develops a discrete‐time joint analytical framework for pricing volatility index (VIX) and VXX options consistently. We show that our framework is more flexible than continuous‐time VXX models as it allows the information contained in the high‐frequency VIX index to be incorporated for the joint pricing of VIX and VXX options, and the joint pricing formula is derived. Our empirical analysis shows that the model that utilizes the realized variance (RV) computed from the high‐frequency VIX index data significantly outperforms the model that does not rely on the VIX RV in the joint pricing both in‐sample and out‐of‐sample, reinforcing the beliefs that high‐frequency data are informative about the derivatives pricing

How do market volatility and risk aversion sentiment inter-influence over time? Evidence from Chinese SSE 50 ETF options

State-dependent intra-day volatility pattern and its impact on price jump detection - Evidence from international equity indices

Abstract We address the construction of Realized Variance (RV) forecasts by exploiting the hierarchical structure implicit in available decompositions of RV. We propose a post-forecasting approach that utilizes bottom-up and regression-based reconciliation methods. By using data referred to the Dow Jones Industrial Average Index and to its constituents we show that exploiting the informative content of hierarchies improves the forecast accuracy. Forecasting performance is evaluated out-of-sample based on the empirical MSE and QLIKE criteria as well as using the Model Confidence Set approach.

Forecasting global stock market volatilities: A shrinkage heterogeneous autoregressive (HAR) model with a large cross-market predictor set

Abstract We use a vector autoregressive model with functional shocks, capturing the shift of the entire term structure of interest rates on monetary policy announcement dates, to empirically evaluate the effects of conventional and unconventional monetary policy decisions on the Real Estate Investment Trusts (REITs) markets of the United States (US). Using 5-min interval intraday data, we analyze not only the impact on REITs returns, but also its realized variance (RV), realized jumps (RJ), realized skewness (RSK), and realized kurtosis (RKU) over the daily period of September 2008 to June 2021. While the effects of conventional monetary policy shocks on the moments of REITs returns tend to conform with economic theories, the same is not necessarily the case with unconventional monetary policy shocks. In addition, though monetary policy shocks have the most persistent and strongest effects on RJ, the extreme behaviour of the REITs market is also observed through RSK and RKU. Moreover, when we look into 10 REITs sectors, there is indeed heterogeneity in terms of the strength of the effect, but not so much in terms of the sign of responses of the various moments compared to the overall market. Our results have important implications for REITs market participants, given its exponential growth as an asset class.

Spreading of cross-market volatility information: Evidence from multiplex network analysis of volatility spillovers

Smooth Transition Exponential Smoothing (STES) is a popular exponential smoothing method for volatility forecasting; whereby the success of the STES model lies in the choice of the transition variable. In this paper, three realized variance (RV), daily, weekly and monthly RV were used as the transition variables in STES methods to evaluate the performance of intraday data. While daily squared return is a noisy series, squared residual and daily RV were employed as the proxy for actual volatilities in this study. With five series of exchange rates, a comparative analysis was conducted for Ad Hoc methods, Generalised Autoregressive Conditional Heteroscedastic (GARCH) models, and STES methods using various RV combinations. The empirical results showed that when daily RV was used as proxy for actual volatility, the traditional STES models and STES models with RV as the transition variables outperformed Ad Hoc methods and GARCH models under the RMSE evaluation criteria. Similar promising results were also observed for traditional STES models and STES models with RV as the transition variables under MAE evaluation. The MCS results generally reaffirmed the results from both the MAE and RMSE evaluation criteria.

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.

We forecast realized variance (RV) of Real Estate Investment Trusts for 10 leading markets and regions, derived from 5-minutes-interval intraday data, based on the information content of two alternative metrics of daily oil-price uncertainty. Based on the period of the analysis covering January 2008 to July 2020, and using variants of the popular MIDAS-RV model, augmented to include oil market uncertainties, captured by its RV (also derived from 5-minute intraday data) and implied volatility (i.e. the oil VIX), we report evidence of significant statistical and economic gains in the forecasting performance. The result is robust to the size of the forecasting samples, including that of the COVID-19 period, lag-length, nonlinearities, asymmetric effects, and forecast horizon. Our results have important implications for investors and policymakers.

Early Warning Systems for identifying financial instability

Abstract Given that jumps in the implied volatility index (VIX) lead to rapid changes in the level of volatility, they may contain significant predictive information for the realized variance (RV) of stock returns. Against this backdrop, the present study proposes to extend the heterogeneous autoregressive (HAR) model using the information content of time‐varying jumps occurring in VIX. We find that jumps in VIX have positive impacts on the RV of S&P 500 index and that the proposed HAR‐RV approach generates more accurate volatility forecasts than do the existing HAR‐RV type models. Importantly, these results hold for short‐, medium‐, and long‐term volatility components.

Improving variance forecasts: The role of Realized Variance features

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.

We examine the predictive value of gold-to-silver and gold-to-platinum price ratios, as proxies for global risks affecting the realized variance (RV) of oil-price movements, using monthly data over the longest available periods of 1915:01–2021:03 and 1968:01–2021:03, respectively. Using the two ratios, we find statistically significant evidence of in-sample predictability for increases in RV for both ratios. This finding also translates into statistically significant out-of-sample forecasting gains derived from these two ratios for RV. Given the importance of real-time forecasts of the volatility of oil-price movements, our results have important implications for investors and policymakers.

We use the heterogenous autoregressive (HAR) model to compute out-of-sample forecasts of the monthly realized variance (RV) of movements of the spot and futures price of heating oil. We extend the HAR–RV model to include the role of El Niño and La Niña episodes, as captured by the Equatorial Southern Oscillation Index (EQSOI). Using data from June 1986 to April 2021, we show evidence for several model configurations that both El Niño and La Niña phases contain information useful for forecasting subsequent to the realized variance of price movements beyond the predictive value already captured by the HAR–RV model. The predictive value of La Niña phases, however, seems to be somewhat stronger than the predictive value of El Niño phases. Our results have important implications for investors, as well as from the perspective of sustainable decisions involving the environment.

Forecasting power of infectious diseases-related uncertainty for gold realized variance

In this paper, we develop a penalized realized variance (PRV) estimator of the quadratic variation (QV) of a high-dimensional continuous Ito 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 bootstrap 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.