A reduced form framework for modeling volatility of speculative prices based on realized variation measures

Building on realized variance and bipower variation measures constructed from high-frequency financial prices, we propose a simple reduced form framework for effectively incorporating intraday data into the modeling of daily return volatility. We decompose the total daily return variability into the continuous sample path variance, the variation arising from discontinuous jumps that occur during the trading day, as well as the overnight return variance. Our empirical results, based on long samples of high-frequency equity and bond futures returns, suggest that the dynamic dependencies in the daily continuous sample path variability are well described by an approximate long-memory HAR–GARCH model, while the overnight returns may be modeled by an augmented GARCH type structure. The dynamic dependencies in the non-parametrically identified significant jumps appear to be well described by the combination of an ACH model for the time-varying jump intensities coupled with a relatively simple log-linear structure for the jump sizes. Finally, we discuss how the resulting reduced form model structure for each of the three components may be used in the construction of out-of-sample forecasts for the total return volatility.     

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.     

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.     

Jump probability using volatility periodicity filters in US Dollar/Euro exchange rates

The discrete daily and intraday jump probabilities of US dollar/euro returns from February 2010 to February 2018 are analyzed using five-minute returns considering several periodicity filters of volatility. When the max outlying statistics are used with Gumbel distribution with periodicity filters such as weighted standard deviation, shortest half scale, and median absolute deviation, the empirical estimates show that the five-minute US dollar/euro returns have lower daily jump probabilities by 13–28% at common critical levels. To detect intraday jumps using the max outlying Gumbel jump statistics, the five-minute US dollar/euro returns have lower daily jump probabilities by 2–10% when the periodicity filters are included at common critical levels. Therefore, when the periodicity filters of volatility are considered, the five-minute US dollar/euro returns have significantly lower daily and intraday jump probabilities than when the periodicity filters are not considered.     

FORECASTING REALIZED VOLATILITY WITH LINEAR AND NONLINEAR UNIVARIATE MODELS

Abstract In this paper, we consider a nonlinear model based on neural networks as well as linear models to forecast the daily volatility of the S&P 500 and FTSE 100 futures. As a proxy for daily volatility, we consider a consistent and unbiased estimator of the integrated volatility that is computed from high‐frequency intraday returns. We also consider a simple algorithm based on bagging (bootstrap aggregation) in order to specify the models analysed in this paper.     

Forecasting exchange rate volatility using high-frequency data: Is the euro different?

We assess the performances of alternative procedures for forecasting the daily volatility of the euro’s bilateral exchange rates using 15 min data. We use realized volatility and traditional time series volatility models. Our results indicate that using high-frequency data and considering their long memory dimension enhances the performance of volatility forecasts significantly. We find that the intraday FIGARCH model and the ARFIMA model outperform other traditional models for all exchange rate series.     

No-arbitrage semi-martingale restrictions for continuous-time volatility models subject to leverage effects,jumps and i.i.d. noise: Theory and testable distributional implications

We develop a sequential procedure to test the adequacy of jump-diffusion models for return distributions. We rely on intraday data and nonparametric volatility measures, along with a new jump detection technique and appropriate conditional moment tests, for assessing the import of jumps and leverage effects. A novel robust-to-jumps approach is utilized to alleviate microstructure frictions for realized volatility estimation. Size and power of the procedure are explored through Monte Carlo methods. Our empirical findings support the jump-diffusive representation for S&P500 futures returns but reveal it is critical to account for leverage effects and jumps to maintain the underlying semi-martingale assumption.     

Hierarchical Markov normal mixture models with applications to financial asset returns

Motivated by the common problem of constructing predictive distributions for daily asset returns over horizons of one to several trading days, this article introduces a new model for time series. This model is a generalization of the Markov normal mixture model in which the mixture components are themselves normal mixtures, and it is a specific case of an artificial neural network model with two hidden layers. The article uses the model to construct predictive distributions of daily S&P 500 returns 1971–2005 and one‐year maturity bond returns 1987–2007. For these time series the model compares favorably with ARCH and stochastic volatility models. The article concludes by using the model to form predictive distributions of one‐ to ten‐day returns during volatile episodes for the S&P 500 and bond return series. Copyright © 2010 John Wiley & Sons, Ltd.     

Jump-robust volatility estimation using nearest neighbor truncation

We propose two new jump-robust estimators of integrated variance that allow for an asymptotic limit theory in the presence of jumps. Specifically, our MedRV estimator has better efficiency properties than the tripower variation measure and displays better finite-sample robustness to jumps and small (“zero”) returns. We stress the benefits of local volatility measures using short return blocks, as this greatly alleviates the downward biases stemming from rapid fluctuations in volatility, including diurnal (intraday) U-shape patterns. An empirical investigation of the Dow Jones 30 stocks and extensive simulations corroborate the robustness and efficiency properties of our nearest neighbor truncation estimators.     

Interdependence between Eastern and Western European stock markets: Evidence from intraday data

We analyze comovements among three stock markets in Central and Eastern Europe and, in addition, interdependence which may exist between Western European (DAX, CAC, UKX) and Central and Eastern European (BUX, PX-50, WIG-20) stock markets. The novelty of our paper rests mainly on the use of 5-min tick intraday price data from mid-2003 to early 2005 for stock indices and on the wide range of econometric techniques employed. We find no robust cointegration relationship for any of the stock index pairs or for any of the extended specifications. There are signs of short-term spillover effects both in terms of stock returns and stock price volatility. Granger causality tests show the presence of bidirectional causality for returns as well as volatility series. The results based on a VAR framework indicate a more limited number of short-term relationships among the stock markets.     

On portfolio optimization: How and when do we benefit from high‐frequency data?

We examine how the use of high‐frequency data impacts the portfolio optimization decision. Prior research has documented that an estimate of realized volatility is more precise when based upon intraday returns rather than daily returns. Using the framework of a professional investment manager who wishes to track the S&P 500 with the 30 Dow Jones Industrial Average stocks, we find that the benefits of using high‐frequency data depend upon the rebalancing frequency and estimation horizon. If the portfolio is rebalanced monthly and the manager has access to at least the previous 12 months of data, daily data have the potential to perform as well as high‐frequency data. However, substantial improvements in the portfolio optimization decision from high‐frequency data are realized if the manager rebalances daily or has less than a 6‐month estimation window. These findings are robust to transaction costs. Copyright © 2009 John Wiley & Sons, Ltd.     

Is there a risk–return trade‐off? Evidence from high‐frequency data

This paper examines the intertemporal relation between risk and return for the aggregate stock market using high‐frequency data. We use daily realized, GARCH, implied, and range‐based volatility estimators to determine the existence and significance of a risk–return trade‐off for several stock market indices. We find a positive and statistically significant relation between the conditional mean and conditional volatility of market returns at the daily level. This result is robust to alternative specifications of the volatility process, across different measures of market return and sample periods, and after controlling for macro‐economic variables associated with business cycle fluctuations. We also analyze the risk–return relationship over time using rolling regressions, and find that the strong positive relation persists throughout our sample period. The market risk measures adopted in the paper add power to the analysis by incorporating valuable information, either by taking advantage of high‐frequency intraday data (in the case of realized, GARCH, and range volatility) or by utilizing the market's expectation of future volatility (in the case of implied volatility index). Copyright © 2006 John Wiley & Sons, Ltd.     

基于GARCH族模型的黄金价格收益率及波动性研究

文章应用GARCH族模型对黄金现货价格的收益率及波动性进行实证研究,实证结果表明黄金价格日收益率具有"尖峰厚尾"和"波动聚类"的特征。通过TGARCH及EGARCH模型发现我国黄金市场存在非对称性现象,正的冲击对黄金价格波动影响更大。     

Fractional integration in daily stock market indices at Jordan's Amman stock exchange

Using daily data on five sectoral indices from 2006 to 2014, this paper aims to investigate the possibility of fractional integration in sectoral returns (and their volatility measures) at Jordan's Amman stock exchange (ASE). Empirical analysis, using the log-periodogram (LP) and local whittle (LW) based semi-parametric fractional differencing techniques suggest that all sectoral returns at ASE exhibit short memory. However, in the case of volatility measures, we found evidence of long memory. Following the recent literature that argues that structural breaks in a time series could also explain the presence of long memory, we tested the volatility measures for the presence of structural breaks. We found that long memory in some volatility measures could be attributed to the presence of structural breaks. Furthermore, using impulse response functions (IRF) based on ARFIMA, we found that shocks to sectoral returns at ASE exhibit short run persistence, whereas shocks to volatility measures display long run persistence.     

Forecasting daily return densities from intraday data: A multifractal approach

This paper proposes a new approach for estimating and forecasting the moments and probability density function of daily financial returns from intraday data. This is achieved through a new application of the distributional scaling laws for the class of multifractal processes. Density forecasts from the new multifractal approach are typically found to provide substantial improvements in predictive ability over existing forecasting methods for the EUR/USD exchange rate, and are also competitive with existing methods when forecasting the daily return density of the S&P500 and NASDAQ-100 equity index.     

Economic indicators and stock market volatility in an emerging economy

By analyzing the daily realized volatility series calculated from intraday stock price observations, this study examines the direct causality between one-day-ahead aggregate stock market volatility and several economic and financial indicators in the Korean market, a leading emerging market. Using the predictive regression and superior predictive ability tests, we find that the model-free implied volatility index (VKOSPI) and stock market indicators both lead the daily market volatility. However, daily economic indicators provide no predictive information beyond that contained in historical volatility. Though in-sample causality does not guarantee a better out-of-sample forecasting performance, the VKOSPI and combinations of predictors exhibit significant predictive ability regardless of the time period. Our study verifies the information role of the VKOSPI as an indicator of daily market risk.     

Dynamics of financial returns densities: A functional approach applied to the Bovespa intraday index

We model the stochastic evolution of the probability density functions (PDFs) of Ibovespa intraday returns over business days, in a functional time series framework. We find evidence that the dynamic structure of the PDFs reduces to a vector process lying in a two-dimensional space. Our main contributions are as follows. First, we provide further insights into the finite-dimensional decomposition of the curve process: it is shown that its evolution can be interpreted as a dynamic dispersion-symmetry shift. Second, we provide an application to realized volatility forecasting, with a forecasting ability that is comparable to those of HAR realized volatility models in the model confidence set framework.     

An investigation of long memory in various measures of stock market volatility, using wavelets and aggregate series

Using methods based on wavelets and aggregate series, long memory in the absolute daily returns, squared daily returns, and log squared daily returns of the S&P 500 Index are investigated. First, we estimate the long memory parameter in each series using a method based on the discrete wavelet transform. For each series, the variance method and the absolute value method based on aggregate series are then employed to investigate long memory. Our findings suggest that these methods provide evidence of long memory in the volatility of the S&P 500 Index. Our esteemed colleague, Robert DiSario, passed away on December 31, 2005.     

Realising the future: forecasting with high‐frequency‐based volatility (HEAVY) models

This paper studies in some detail a class of high‐frequency‐based volatility (HEAVY) models. These models are direct models of daily asset return volatility based on realised measures constructed from high‐frequency data. Our analysis identifies that the models have momentum and mean reversion effects, and that they adjust quickly to structural breaks in the level of the volatility process. We study how to estimate the models and how they perform through the credit crunch, comparing their fit to more traditional GARCH models. We analyse a model‐based bootstrap which allows us to estimate the entire predictive distribution of returns. We also provide an analysis of missing data in the context of these models. Copyright © 2010 John Wiley & Sons, Ltd.     

Do high-frequency measures of volatility improve forecasts of return distributions?

Many finance questions require the predictive distribution of returns. We propose a bivariate model of returns and realized volatility (RV), and explore which features of that time-series model contribute to superior density forecasts over horizons of 1 to 60 days out of sample. This term structure of density forecasts is used to investigate the importance of: the intraday information embodied in the daily RV estimates; the functional form for log(RV)$log\left(RV\right)$ dynamics; the timing of information availability; and the assumed distributions of both return and log(RV)$log\left(RV\right)$ innovations. We find that a joint model of returns and volatility that features two components for log(RV)$log\left(RV\right)$ provides a good fit to S&P 500 and IBM data, and is a significant improvement over an EGARCH model estimated from daily returns.