A common factor of stochastic volatilities between oil and commodity prices

This article analyses the multivariate stochastic volatilities (SVs) with a common factor influencing volatilities in the prices of crude oil and agricultural commodities, used for both biofuel and nonbiofuel purposes. Modelling the volatility is crucial because the volatility is an important variable for asset allocation, risk management and derivative pricing. We develop a SV model comprising a latent common volatility factor with two asymptotic regimes with a smooth transition between them. In contrast to conventional volatility models, SVs are generated by the logistic transformation of latent factors, which comprise two components: the common volatility factor and an idiosyncratic component. We present a SV model with a common factor for oil, corn and wheat from 8 August 2005 to 10 October 2014, using a Markov chain Monte Carlo method to estimate the SVs and extract the common volatility factor. We find that the volatilities of oil and grain markets are persistent. According to the estimated common volatility factor, high volatility periods match the 2007–2009 recession and the 2007–2008 financial crisis quite well. Finally, the extracted common volatility factor exhibits a distinct pattern.     

Evaluating and improving GARCH-based volatility forecasts with range-based estimators

This article investigates the feasibility of using range-based estimators to evaluate and improve Generalized Autoregressive Conditional Heteroscedasticity (GARCH)-based volatility forecasts due to their computational simplicity and readily availability. The empirical results show that daily range-based estimators are sound alternatives for true volatility proxies when using Superior Predictive Ability (SPA) test of Hansen (2005) to assess GARCH-based volatility forecasts. In addition, the inclusion of the range-based estimator of Garman and Klass (1980) can significantly improve the forecasting performance of GARCH-t model.     

Empirical Evidence of the Leverage Effect in a Stochastic Volatility Model: A Realized Volatility Approach

Increasing attention has been focused on the analysis of the realized volatility, which can be treated as a proxy for the true volatility. In this paper, we study the potential use of the realized volatility as a proxy in a stochastic volatility model estimation. We estimate the leveraged stochastic volatility model using the realized volatility computed from five popular methods across six sampling-frequency transaction data (from 1-min to 60- min) based on the trust region method. Availability of the realized volatility allows us to estimate the model parameters via the MLE and thus avoids computational challenge in the high dimensional integration. Six stock indices are considered in the empirical investigation. We discover some consistent findings and interesting patterns from the empirical results. In general, the significant leverage effect is consistently detected at each sampling frequency and the volatility persistence becomes weaker at the lower sampling frequency.     

Jumps and volatility dynamics in agricultural commodity spot prices

The spot commodities market exhibits both extreme volatility and price spikes, which lead to heavy-tailed distributions of price change and autocorrelation. This article uses various Lévy jump models to capture these features in a panel of agricultural commodities observed between January 1990 and February 2014. The results show that Levy jump models outperform the continuous Gaussian model. Our results prove that assuming a constant volatility or even a deterministic volatility and drift structure of agricultural commodity spot prices is not realistic and is less efficient than the stochastic assumption. The findings demonstrate an interesting correlation between volatility and jumps for a given commodity i, but no relationship between the volatility of commodity i and the probability of jumps of commodity j.     

Estimation of Asymmetric Stochastic Volatility Models for Stock-Exchange Index Returns

The objective of this paper is to put forward a new autoregressive asymmetric stochastic volatility model for modeling volatility and to compare results obtained for this model with an autoregressive stochastic model and another asymmetric volatility model, such as, asymmetric generalized autoregressive conditional heteroskedasticity model. The results obtained from the estimation by maximum likelihood have shown the volatility behavior is asymmetric in the majority of cases. This fact is better shown by the ARSVA model, than the rest of alternative models. Moreover, the ARSVA model is able to reproduce other stylized facts of such series, such as high kurtosis, no autocorrelation of returns, slow decreasing of the autocorrelation function of the squared returns and high persistence.

Forecasting stock market volatility and information content of implied volatility index

This study investigates the incremental information content of implied volatility index relative to the GARCH family models in forecasting volatility of the three Asia-Pacific stock markets, namely India, Australia and Hong Kong. To examine the in-sample information content, the conditional variance equations of GARCH family models are augmented by incorporating implied volatility index as an explanatory variable. The return-based realized variance and the range-based realized variance constructed from 5-min data are used as proxy for latent volatility. To assess the out-of-sample forecast performance, we generate one-day-ahead rolling forecasts and employ the Mincer–Zarnowitz regression and encompassing regression. We find that the inclusion of implied volatility index in the conditional variance equation of GARCH family model reduces volatility persistence and improves model fitness. The significant and positive coefficient of implied volatility index in the augmented GARCH family models suggests that it contains relevant information in describing the volatility process. The study finds that volatility index is a biased forecast but possesses relevant information in explaining future realized volatility. The results of encompassing regression suggest that implied volatility index contains additional information relevant for forecasting stock market volatility beyond the information contained in the GARCH family model forecasts.     

Modelling the dynamics of Bitcoin and Litecoin: GARCH versus stochastic volatility models

We examine and compare a large number of generalized autoregressive conditional heteroskedastic (GARCH) and stochastic volatility (SV) models using series of Bitcoin and Litecoin price returns to assess the model fit for dynamics of these cryptocurrency price returns series. The various models examined include the standard GARCH(1,1) and SV with an AR(1) log-volatility process, as well as more flexible models with jumps, volatility in mean, leverage effects, t-distributed and moving average innovations. We report that the best model for Bitcoin is SV-t while it is GARCH-t for Litecoin. Overall, the t-class of models performs better than other classes for both cryptocurrencies. For Bitcoin, the SV models consistently outperform the GARCH models and the same holds true for Litecoin in most cases. Finally, the comparison of GARCH models with GARCH-GJR models reveals that the leverage effect is not significant for cryptocurrencies, suggesting that these do not behave like stock prices.     

Asset prices and economic fluctuations: The implications of stochastic volatility

This paper investigates whether the multi-factor stochastic volatility of stock returns is related to economic fluctuations and affects asset prices. We address these issues in a dynamic Fama-French three-factor volatility model framework. Consistent with the ICAPM with stochastic volatility (Campbell et al., 2017), we find that the conditional volatility of the size and value factors is significantly related to economic uncertainty. These volatilities are also significant pricing factors. The out-of-sample forecasting analysis further reveals that the conditional volatility can predict stock returns and deliver economic gain in asset allocation. Our analysis sharpens the understanding on the link between the stock market and economic fundamentals.     

Smiling under stochastic volatility

This paper studies the behavior of the implied volatility function (smile) when the true distribution of the underlying asset is consistent with the stochastic volatility model proposed by Heston (1993). The main result of the paper is to extend previous results applicable to the smile as a whole to alternative degrees of moneyness. The conditions under which the implied volatility function changes whenever there is a change in the parameters associated with Hestons stochastic volatility model for a given degree of moneyness are given.JEL Classification: G12, G13Mathematical assistance provided by José Alcalde (Universidad de Alicante) is much appreciated, and we have also benefited from discussions with Eva Ferreira (Universidad del País Vasco) and Javier Fernández Navas (Instituto de Empresa). We also thank José M. Campa (IESE) and two anonymous referees, whose suggestions have helped us improve this paper substantially. Gonzalo Rubio and Ángel León acknowledge the financial support provided by Ministerio de Ciencia y Tecnología grants BEC2001-0636 and BEC2002-03797 respectively. Ángel León also acknowledges Generalitat Valenciana grant CTIDIA/2002/103. The contents of this paper are the sole responsibility of the authors.     

Cyclicality of stock market volatility

By utilizing the significance and stochastic dominance tests, this paper formally tests the relationship between stock market volatility and the business cycle. Results show that, for most matured markets, stock market volatility is countercyclical, while for emerging markets, the volatility can be procyclical.     

Testing for a unit root in the presence of stochastic volatility and leverage effect

Previous studies have shown that the stationary and nonstationary time-varying volatilities have different implications on the unit root test. In this paper, we provide a Bayesian unit root test for an AR(1) model with stochastic volatility and leverage effect. Monte Carlo simulations show that the proposed Bayesian unit root test statistic achieves good finite sample properties and is robust to the stationarity of stochastic volatility.     

Volatility transmission between Japan,UK and USA in daily stock returns

In the past, there are a lot of studies which conclude that the holiday, asymmetry and day-of-the-week effects influence stock price volatility. Most of the studies are based on a class of generalized auto-regressive conditional heteroskedasticity (GARCH) models. No one examines these effects simultaneously using stochastic volatility (SV) models. In this paper, using the SV model, we examine whether these effects play an important role in stock price volatilities. Furthermore, we consider spillover effects between Japan, UK and USA, where spillover effects in price level as well as volatility are taken into account. We are grateful to two anonymous referees for suggestions and comments. We also acknowledge Toshiaki Watanabe who gave us a lot of helpful suggestions and comments in the preliminary version of this paper. This research is partially supported from Japan Society for the Promotion of Science (Grant-in-Aid for Scientific Research (C) #18530158, 2006–2009, and Grant-in-Aid for COE Research) and the Zengin Foundation (Grant-in-Aid for Studies on Economics and Finance), which are acknowledged by H. Tanizaki.     

Forecasting the oil futures price volatility: A new approach

This study provides a new perspective of modelling and forecasting realized range-based volatility (RRV) for crude oil futures. We are the first to improve the Heterogeneous Autoregressive model of Realized Range-based Volatility (HAR-RRV) model by considering the significant jump components, signed returns and volatility of realized range-based volatility. The empirical results show that the volatility of volatility significantly exists in the oil futures market. Moreover, our new proposed models with significant jump components, signed returns and volatility of volatility can gain higher forecast accuracy than HAR-RRV-type models. The results are robust to different forecasting windows and forecasting horizons. Our new findings are strategically important for investors making better decisions.     

中国宏观经济波动的结构性转变与启示

本文研究改革开放以来30年间中国主要宏观经济指标的季度时序波动性特征。笔者将时变参数随机波动模型应用于离散型时序分析,并运用存在干扰系数情况下的内生断点检验方法来正确识别不同经济指标波动性特征发生结构性变化的准确时间。研究结果表明,经济增长、通货膨胀、货币供给以及有效汇率等主要宏观经济指标的波动特征在20世纪90年代中期均发生显著结构性转变,宏观政策的系统性改进是这些变化的主要动因。     

Business cycle fluctuations in Taiwan — A Bayesian DSGE analysis

This paper examines the Taiwanese economy in a small open economy DSGE model using Bayesian estimation. The model consists of two countries and 12 exogenous shocks with stochastic volatility to capture the fluctuations in the business cycle. The main results are: (1) shock innovations with stochastic volatility increase the model fit, (2) shocks originated from outside the country are important sources of fluctuations in the Taiwanese business cycle.     

S&P500 volatility analysis using high-frequency multipower variation volatility proxies

The availability of ultra-high-frequency data has sparked enormous parametric and nonparametric volatility estimators in financial time series analysis. However, some high-frequency volatility estimators are suffering from biasness issues due to the abrupt jumps and microstructure effect that often observed in nowadays global financial markets. Hence, we motivate our studies with two long-memory time series models using various high-frequency multipower variation volatility proxies. The forecast evaluations are illustrated using the S&P500 data over the period from year 2008 to 2013. Our empirical studies found that higher-power variation volatility proxies provide better in-sample and out-of-sample performances as compared to the widely used realized volatility and fractionally integrated ARCH models. Finally, these empirical findings are used to estimate the one-day-ahead value-at-risk of S&P500.     

FORECASTING GLOBAL EQUITY INDICES USING LARGE BAYESIAN VARS

This paper proposes a large Bayesian Vector Autoregressive (BVAR) model with common stochastic volatility to forecast global equity indices. Using a monthly dataset on global stock indices, the BVAR model controls for co‐movement commonly observed in global stock markets. Moreover, the time‐varying specification of the covariance structure accounts for sudden shifts in the level of volatility. In an out‐of‐sample forecasting application we show that the BVAR model with stochastic volatility significantly outperforms the random walk both in terms of point as well as density predictions. The BVAR model without stochastic volatility, on the other hand, shows some merits relative to the random walk for forecast horizons greater than six months ahead. In a portfolio allocation exercise we moreover provide evidence that it is possible to use the forecasts obtained from our model with common stochastic volatility to set up simple investment strategies. Our results indicate that these simple investment schemes outperform a naive buy‐and‐hold strategy.     

A new generalized volatility proxy via the stochastic volatility model

This article proposes power transformation of absolute returns as a new proxy of latent volatility in the stochastic model. We generalize absolute returns as a proxy for volatility in that we place no restriction on the power of absolute returns. An empirical investigation on the bias, mean square error and relative bias is carried out for the proposed proxy. Simulation results show that the new estimator exhibiting negligible bias appears to be more efficient than the unbiased estimator with high variance.     

On the predictive power of ARJI volatility forecasts for Bitcoin

Motivated by the recent literature on cryptocurrency volatility dynamics, this paper adopts the ARJI, GARCH, EGARCH, and CGARCH models to explore their capabilities to make out-of-sample volatility forecasts for Bitcoin returns over a daily horizon from 2013 to 2018. The empirical results indicate that the ARJI jump model can cope with the extreme price movements of Bitcoin, showing comparatively superior in-sample goodness-of-fit, as well as out-of-sample predictive performance. However, due to the excessive volatility swings on the cryptocurrency market, the realized volatility of Bitcoin prices is only marginally explained by the GARCH genre of employed models.     

FINANCIAL DEVELOPMENT AND MACROECONOMIC VOLATILITY

Using cross‐country panel data over the period 1996–2012, this paper examines the impact of financial development on macroeconomic volatility using GMM estimators. In contrast to the linear relationship identified in many previous studies, we present robust evidence suggesting that the effect of financial development on macroeconomic volatility is nonlinear and U‐shaped. We also investigate the potential differences between developed and developing countries. The results of the paper add new evidence and shed interesting insights into the recent debate on the role of finance in macroeconomic fluctuations.