Forecasting the realized volatility in the Chinese stock market: further evidence

In this study, the impact of noise and jump on the forecasting ability of volatility models with high-frequency data is investigated. A signed jump variation is added as an additional explanatory variable in the volatility equation according to the sign of return. These forecasting performances of models with jumps are compared with those without jumps. Being applied to the Chinese stock market, we find that the jump variation has a significant in-sample predictive power to volatility and the predictive power of the negative one is greater than the positive one. Furthermore, out-of-sample evidence based on the fresh model confidence set (MCS) test indicates that the incorporation of singed jumps in volatility models can significantly improve their forecasting ability. In particular, among the realized variance (RV)-based volatility models and generalized autoregressive conditional heteroscedasticity (GARCH) class models, the heterogeneous autoregressive model of realized volatility (HAR-RV) model with the jump test and a decomposed signed jump variation have better out-of-sample forecasting performance. Finally, the use of the decomposed signed jump variations in predictive regressions can improve the economic value of realized volatility forecasts.     

A bootstrap test for jumps in financial economics

An i.i.d. bootstrap is applied for the ratio test of Barndorff-Nielsen and Shephard (2006) for jumps in jump diffusion processes. Asymptotic validity is established for the bootstrap test both under the null of no jump and under the alternative of jumps. Finite sample simulation shows that the bootstrap test has more stable size than the ratio test of Barndorff-Nielsen and Shephard (2006).     

House price dynamics,conditional higher-order moments,and density forecasts

Most studies on housing price dynamics are only concerned with the conditional mean and variance, but overlook other higher-order conditional moments and the structural change characteristics inherent in housing prices. In order to take into account these two important issues, this study utilizes the generalized Markov switching GARCH model to explore house price dynamics and conditional distribution for US market over 1975Q1–2007Q4. The housing return follows two distinct dynamics: the bust regime and the boom regime. The volatility pattern is different in the bust and boom regimes. In addition, the conditional densities derived by the regime-switching model change dramatically over time and are significantly different from normal distribution. More importantly, the regime-switching model can detect in advance a weak US housing market such as the one that occurred in the middle of 2007. The in-sample fitting ability of regime-switching model, which incorporates higher-order moments, has significant improvements compared to the single-regime AR and AR-GARCH models. For the out-of-sample Value-at-Risk forecasting performance, the ability of regime-switching AR-GARCH model to forecast one-step-ahead density is better compared to the single-regime AR-GARCH model.     

A correlated bivariate Poisson jump model for foreign exchange

This paper develops a new bivariate jump model to study jump dynamics in foreign exchange returns. The model extends a multivariate GARCH parameterization to include a bivariate correlated jump process. The conditional covariance matrix has the Baba, Engle, Kraft, and Kroner (1989) structure, while the bivariate jumps are governed by a Correlated Bivariate Poisson (CBP) function. Using daily data we find evidence of both independent currency specific jumps, as well as jumps common to both exchange rates of the Canadian dollar and Japanese Yen against the U.S. dollar. The paper concludes by investigating a time-varying structure for the arrival of jumps that relaxes the assumption of constant and bounded jump correlation imposed by the CBP function.I am indebted to two anonymous referees and the editor, Baldev Raj for helpful suggestions. I am also grateful for helpful comments from Adolf Buse, Ramazan Gencay, Rehim Kilic, John Maheu, Alex Maynard, Denis Pelletier, Denise Young, and seminar participants at the Tenth Annual Symposium of the Society for Nonlinear Dynamics and Econometrics (SNDE), Federal Reserve Bank of Atlanta 2002; the Midwest Econometrics Group (MEG) Meetings, Federal Reserve Bank of Kansas City 2001; Canadian Economics Association (CEA) Meetings, McGill University 2001.     

Pricing Nikkei 225 Options Using Realized Volatility

This article examines option pricing performance using realized volatilities with or without handling microstructure noise, non‐trading hours and large jumps. The dynamics of realized volatility is specified by ARFIMA(X) and HAR(X) models. The main results using put options on the Nikkei 225 index are that: (i) the ARFIMAX model performs best; (ii) the Hansen and Lunde (2005a) adjustment for non‐trading hours improves the performance; (iii) methods for reducing microstructure noise‐induced bias yield better performance, while if the Hansen–Lunde adjustment is used, the other methods are not necessarily needed; and (iv) the performance is unaffected by removing large jumps from realized volatility.     

QUANTILE FORECASTS OF FINANCIAL RETURNS USING REALIZED GARCH MODELS*

This article applies the realized generalized autoregressive conditional heteroskedasticity (GARCH) model, which incorporates the GARCH model with realized volatility, to quantile forecasts of financial returns, such as Value‐at‐Risk and expected shortfall. Student's t‐ and skewed Student's t‐distributions as well as normal distribution are used for the return distribution. The main results for the S&P 500 stock index are: (i) the realized GARCH model with the skewed Student's t‐distribution performs better than that with the normal and Student's t‐distributions and the exponential GARCH model using the daily returns only; and (ii) using the realized kernel to take account of microstructure noise does not improve the performance.     

Conditional volatility and correlations of weekly returns and the VaR analysis of 2008 stock market crash

Modelling of conditional volatilities and correlations across asset returns is an integral part of portfolio decision making and risk management. Over the past three decades there has been a trend towards increased asset return correlations across markets, a trend which has been accentuated during the recent financial crisis. We shall examine the nature of asset return correlations using weekly returns on futures markets and investigate the extent to which multivariate volatility models proposed in the literature can be used to formally characterize and quantify market risk. In particular, we ask how adequate these models are for modelling market risk at times of financial crisis. In doing so we consider a multivariate t version of the Gaussian dynamic conditional correlation (DCC) model proposed by Engle (2002), and show that the t-DCC model passes the usual diagnostic tests based on probability integral transforms, but fails the value at risk (VaR) based diagnostics when applied to the post 2007 period that includes the recent financial crisis.     

金融资产收益率波动预测——基于我国股票市场跳跃行为研究

金融资产收益率波动是资产定价和金融风险管理的核心部分,而跳跃是收益率波动中的重要组成部分。基于修正Z-检验,本文检测识别我国股市波动中跳跃行为,并且研究了跳跃的时序特征,统计结果表明,在市场大波动时期,和连续成份相比,跳跃对于波动率具有极其重要的贡献。建立包含跳跃的已实现波动率非齐次自回归模型,在波动模型中纳入滞后绝对日收益率和杠杆效应预测股指收益率波动。实证分析结果显示,对于短期的波动预测,包含跳跃和两种影响因素的波动模型表现最好,然而对于提前1月的长期预测,跳跃和连续波动成份分离模型预测明显优于其它模型,这些事实说明跳跃对股指波动率预测具有重要的影响,好坏消息对波动率非对称性具有短期显著影响,而对长期水平的波动率预测影响不显著。     

Realized volatility transmission: The role of jumps and leverage effects

This paper is the first to employ a multivariate extension of the LHAR–CJ model for realized volatility of Corsi and Renó (2012) considering continuous and jump volatility components and leverage effects. The model is applied to financial (S&P 500), commodity (WTI crude oil) and forex (US$/EUR) intraday futures data and allows new insights in the transmission mechanisms among these markets. Besides significant leverage effects, we find that the jump components of all considered assets do not contain incremental information for the one-step ahead realized volatility. The volatility of S&P 500 and US$/EUR exchange rate futures exhibits significant spillovers to the realized volatility of WTI. Moreover, decreasing equity prices appear to increase volatility in other markets, while strengthening of the US$ seems to calm down the crude oil market.     

Volatility spill-overs in commodity spot prices: New empirical results

The classical rational expectations model of commodity markets implies that expected spot price risk is an explanatory variable in spot price regressions; and also that inventory carryover, which is reduced by a larger price variance, creates autoregressive conditional heteroscedastic processes in spot prices. In order to falsify/verify this theory, it has typically been assumed that the square root of the conditional variance of spot prices, a proxy for spot price risk, enters the conditional mean function of spot prices. Based on this simple representation, a typical but counter intuitive outcome has been that spot price risk has an insignificant impact on spot prices, see, e.g., Beck (Beck, S., 1993. A Rational Expectations Model of Time Varying Risk Premia in Commodities Futures Markets: Theory and Evidence. International Economic Review 34, 149–168, Beck, S., 2001. Autoregressive Conditional Heteroskedasticity in Commodity Spot Prices. Journal of Applied Econometrics 16, 115–132). In this paper, we propose an alternative functional relationship (from GARCH(1,1) to GARCH(1,1)-AR(m)) between spot price risk and spot prices that is fully supported by the classical rational expectations model, and based on this new representation we are able to provide stronger empirical support for Muth's rational expectation theory.     

Twenty years of jumps in commodity markets

In this article, we provide statistical evidence around jumps affecting commodity returns. Using nearly 20 years of daily data, we use Laurent, Lecourt, and Palm's (2011) methodology to jump extraction, and discuss various aspects of the estimated jump activity. On average across various commodity markets, we find a high number of days for which returns exhibit the presence of jumps, consistently with the intuition that commodities are affected by large price fluctuations. We emphasize that the post-jump average return depends on the commodity sector considered (e.g. agriculture, energy, or metals). We also show evidence of a jump-to-volatility channel for commodities (similar to the effect usually found for equities). Finally, we diagnose around 40 dates during which commodity indices, stocks, bonds and currencies `co-jump’, revealing a tail dependence between standard and alternative assets.     

The risk-return relation and VIX: evidence from the S&P 500

A significantly positive risk-return relation for the S&P 500 market index is detected if the squared implied volatility index (VIX) is allowed for as an exogenous variable in the conditional variance equation of the parsimonious GARCH(1,1) model. This result holds for both daily and weekly observations, for extended conditional mean and variance specifications, and is robust to sub-samples. We show that the conditional variance obtained from the GARCH model with VIX has better predictive ability for realized volatility than the conditional variance from GARCH without VIX and VIX itself, thereby documenting an important information content of VIX for conditional variance. The results are interpreted as evidence that adding VIX squared in the conditional variance equation yields a better measure of conditional variance which, subsequently, uncovers a strong risk-return relation.     

Using monthly returns to model conditional heteroscedasticity

This empirical study examines the extent of non–linearity in a multivariate model of monthly financial series. To capture the conditional heteroscedasticity in the series, both the GARCH(1,1) and GARCH(1,1)–in–mean models are employed. The conditional errors are assumed to follow the normal and Student– t distributions. The non–linearity in the residuals of a standard OLS regression are also assessed. It is found that the OLS residuals as well as conditional errors of the GARCH models exhibit strong non–linearity. Under the Student density, the extent of non–linearity in the GARCH conditional errors was generally similar to those of the standard OLS. The GARCH–in–mean regression generated the worse out–of–sample forecasts.     

Forecasting the volatility of crude oil futures using high-frequency data: further evidence

We forecast the realized volatility of crude oil futures market using the heterogeneous autoregressive model for realized volatility and its various extensions. Out-of-sample findings indicate that the inclusion of jumps does not improve the forecasting accuracy of the volatility models, whereas the “leverage effect” pertaining to the difference between positive and negative realized semi-variances can significantly improve the forecasting accuracy in predicting the short- and medium-term volatility. However, the signed jump variations and its decomposition couldn’t significantly enhance the models’ forecasting accuracy on the long-term volatility.     

Autoregressive conditional durations: An application to the Surinamese dollar versus the US dollar exchange rate

The parallel market nominal exchange rate of the United States dollar vis-à-vis the Surinamese dollar (USD/SRD) exhibited periods of severe volatility which were often followed by episodes of stability, usually at a cost of sharp depreciations. This study seeks to model this exchange rate using autoregressive conditional duration models. These models are suitable for modelling events occurring with irregular intervals. Exchange rates in developing countries have distinct features compared to exchange rates in countries with well-established and accessible financial markets. A key feature is that for these developing countries, exchange rates only occasionally experience jumps. Our findings suggest that past exchange rate changes appear to be a significant driver of future exchange rate jumps. Furthermore, our results show that money, international reserves, and commodity prices can explain jumps in the market USD/SRD exchange rate.     

ALLOWING FOR JUMP MEASUREMENTS IN VOLATILITY: A HIGH‐FREQUENCY FINANCIAL DATA ANALYSIS OF INDIVIDUAL STOCKS

Following recent advances in the non‐parametric realized volatility approach, we separately measure the discontinuous jump part of the quadratic variation process for individual stocks and incorporate it into heterogeneous autoregressive volatility models. We analyse the distributional properties of the jump measures vis‐à‐vis the corresponding realized volatility ones, and compare them to those of aggregate US market index series. We also demonstrate important gains in the forecasting accuracy of high‐frequency volatility models.     

The impact of interest rate and exchange rate volatility on banks' stock returns and volatility: Evidence from Turkey

This paper investigates the effects of interest rate and foreign exchange rate changes on Turkish banks' stock returns using the OLS and GARCH estimation models. The results suggest that interest rate and exchange rate changes have a negative and significant impact on the conditional bank stock return. Also, bank stock return sensitivities are found to be stronger for market return than interest rates and exchange rates, implying that market return plays an important role in determining the dynamics of conditional return of bank stocks. The results further indicate that interest rate and exchange rate volatility are the major determinants of the conditional bank stock return volatility.     

LABOR MOBILITY OF IMMIGRANTS: TRAINING,EXPERIENCE, LANGUAGE,AND OPPORTUNITIES*

This article analyzes the labor mobility and human capital accumulation of male immigrants from the former Soviet Union to Israel. We estimate a dynamic choice model for employment and training in blue‐ and white‐collar occupations, where the labor market randomly offered opportunities are affected by past choices. The estimated model accurately reproduces the patterns in the data. The estimated direct earning return to local training, local experience, and knowledge of Hebrew are very high, whereas imported skills have zero (conditional) return. The welfare gain from the impact of training on job offer probabilities is larger than its effect on wages.     

BAYESIAN ANALYSIS OF GENERALIZED AUTOREGRESSIVE CONDITIONAL HETEROSKEDASTICITY AND STOCHASTIC VOLATILITY: MODELING LEVERAGE,JUMPS AND HEAVY‐TAILS FOR FINANCIAL TIME SERIES*

This paper develops a Bayesian model comparison of two broad major classes of varying volatility model, the generalized autoregressive conditional heteroskedasticity and stochastic volatility models, on financial time series. The leverage effect, jumps and heavy‐tailed errors are incorporated into the two models. For estimation, the efficient Markov chain Monte Carlo methods are developed and the model comparisons are examined based on the marginal likelihood. The empirical analyses are illustrated using the daily return data of US stock indices, individual securities and exchange rates of UK sterling and Japanese yen against the US dollar. The estimation results indicate that the stochastic volatility model with leverage and Student‐t errors yield the best performance among the competing models.     

Liquidity-adjusted conditional capital asset pricing model

This paper derives a liquidity-adjusted conditional two-moment capital asset pricing model (CAPM) and a liquidity-adjusted conditional three-moment CAPM respectively based on theory of stochastic discount factor. The liquidity-adjusted conditional two-moment CAPM shows that a security's conditional expected excess return consists of three parts: its conditional expected liquidity cost, the systemic risk premium and the liquidity risk premium. The liquidity-adjusted conditional three-moment CAPM shows that a security's conditional expected excess return depends on its conditional expected liquidity cost, the conditional covariance between its return and the market return, the conditional covariance between its liquidity cost and the market liquidity cost, and the conditional coskewness of its return and the market return.