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This paper investigates the asymmetric characteristics of returns and volatilities of various Chinese commodity futures within the threshold stochastic volatility (THSV) framework with various distribution assumptions. To gauge the capabilities of THSV models in volatility forecasting, the values-at-risk (VaRs) for both long and short positions in these futures are estimated and analyzed. We demonstrate that the asymmetric THSV model outperforms the corresponding symmetric SV model, and that the THSV models with non-normal distributions can better fit the futures data than the standard THSV model. Our results clearly indicate that positive and negative news have asymmetric effects on the mean, variance, and variance persistence of all futures under consideration. We also document that modeling both the mean and variance asymmetries and the fat-tailed feature in return distributions is particularly important to accurately forecast the VaRs for long and short trading positions in commodity futures.

It is documented in the literature that asset returns and volatilities respond differently to bad news than to good news. In particular, a negative market shock typically has a stronger impact on returns and volatilities than does a positive shock of the same magnitude. A profound understanding of this asymmetric effect is important to investors and risk managers, as it helps better characterize return dynamics and accurately forecast future volatilities, which are critical inputs to risk management and asset pricing models. The purpose of this paper is to investigate the asymmetric characteristics of returns and volatilities in Chinese commodity futures markets for copper, aluminum, natural rubber, and soybeans. The asymmetric feature in asset means is first examined by Black (1976), who finds that an increase in implied volatility leads to a decline in returns greater in absolute magnitude than the increase in returns corresponding to a decrease in implied volatility of equivalent magnitude. Subsequently, many studies (Bekaert and Wu, 2000, Cappiello et al., 2006, Christie, 1982, Engle and Ng, 1993, Glosten et al., 1993, Nelson, 1991, Thomakos et al., 2008 and Wu, 2001) explore the asymmetric response in volatilities of equity returns to good versus bad news in terms of positive versus negative lagged returns without explaining the origin of the news, and document that this volatility asymmetry is predominately attributed to either the leverage or the volatility feedback effect. The literature also finds that correlations among asset returns often increase when asset return volatilities rise or when the market is in a downturn (Ang and Chen, 2002, Bae et al., 2003, Karolyi and Stulz, 1996 and Kroner and Ng, 1998). However, the research in this area focuses primarily on the equity market, with little work conducted on futures markets except by Perrakis and Khoury (1998) and Lien and Yang (2006). Perrakis and Khoury (1998) examine the theoretical and empirical implications of asymmetric information in canola, barley, and oats futures contracts, traded on the Winnipeg Commodity Exchange (WCE), and show that there is information asymmetry with known spot supplies in canola and barley. Lien and Yang (2006) explore the asymmetric effects of positive and negative spot-futures spreads on the return and the risk structure of currency spot and futures markets using a bivariate dynamic conditional correlation GARCH framework. In contrast with previous studies, this paper intends to characterize both return and variance dynamics of various Chinese commodity futures, accounting for both the fat-tailed feature and asymmetric effects. To this end, we adopt the threshold stochastic volatility (THSV) approach proposed by So et al. (2002), and extend it to cases in which alternative distributions are allowed. In theory, the THSV approach is more flexible in describing mean and variance asymmetries in time series than is the threshold ARCH type model (Li and Lam, 1995, So et al., 2002 and Xu, 2012). In particular, the asymmetric ARCH type model focuses on asymmetries in returns or volatilities alone, while the THSV approach enables us to investigate three asymmetric effects simultaneously: the asymmetries in returns, volatilities, as well as volatility persistence. So and Choi (2009) examine the Hong Kong stock market using the advanced threshold factor multivariate stochastic volatility (TFMSV) model, and confirm that the THSV approach can adequately capture asymmetries in both stock return and variance dynamics. For this reason, the THSV approach has received more attention in most recent empirical work. For example, Xu (2012) simulates and analyzes the Hang Seng Index (HSI), Nikkei 225 Index (Nikkei 225), and Standard & Poor's 500 (S&P 500) Index, while Liu and Zhou (2012) examine the asymmetric effects of risky events on Chinese stock markets using the standard THSV model. The standard THSV model assumes a normal return distribution, which fails to capture the non-normal properties observed in real data, such as skewness and excess kurtosis. Thus, this paper considers the student-t, generalized error, and mixture of normal distributions in the THSV model to better capture observed distribution characteristics in futures data. To estimate the THSV model, we apply the Bayesian Markov chain Monte Carlo (MCMC) technique. The key to this method is to draw all parameters from their full conditional posterior distributions using Gibbs sampling procedure, which helps improve the efficiency of parameter estimation (Eraker et al., 2003). It is shown that the MCMC approach results in a smaller estimation error and a smaller root mean squared error than do other estimation approaches, such as the efficient method of moments (EMM), generalized method of moments (GMM), and quasi-maximum likelihood estimation (QMLE) (Andersen et al., 1999 and Jacquier et al., 1994). Based on the deviance information criterion (DIC), we first assess the performance of the asymmetric THSV model compared with the symmetric SV model to gauge the advantages of modeling mean and variance asymmetries. We also document the importance of incorporating these asymmetries and non-normal properties into the THSV approach to better fit futures data. With the most appropriate model, we then analyze the size, direction, and statistical significance of various asymmetric effects in our futures data series. We further evaluate the ability of various models to forecast the one-day-ahead value-at-risk (VaR) for long and short trading positions in the commodity futures considered. Backtesting is conducted to evaluate their relative performance, and thereby to see whether incorporating asymmetric effects and the fat-tailed feature into these models can help improve the accuracy of VaR forecasting. The VaR or the VaR for long positions, by definition, focuses solely on the downward tail of the return distribution, addressing the major concern of potential losses resulting from price drops for an investor who holds a long position in assets. On the other hand, the VaR for short positions measures investors' losses incurred by increases in asset prices. Most previous work on asymmetric characteristics of asset returns is based on model specifications and estimation results rather than on the model's out-of-sample performance. In contrast, by looking at the VaRs for both long and short positions, we evaluate a model's out-of-sample performance in modeling both large negative and positive returns. Moreover, previous research on this subject focuses primarily on equity markets, whereas this paper explores asymmetric distribution properties of Chinese commodity futures on copper, aluminum, natural rubber, and soybeans. With the dramatic growth of the Chinese economy over the past three decades, Chinese financial markets have become increasingly important in international markets. According to the Futures Industry Association (FIA), in 2008 the trading volume of Chinese commodity futures was 36.5% of the world's total trading volume, and China’s is now the second largest commodity futures market in the world, with the US market being the largest.1 However, there are significant structural and institutional differences between Chinese markets and developed markets. Thus, from an empirical perspective, Chinese futures may exhibit unique return characteristics, and as such are an interesting case for research. Surprisingly, not much research has been conducted on Chinese commodity futures markets to date. In terms of DIC values, our results show that the asymmetric THSV model outperforms the symmetric SV model given the same distribution assumption, and that the THSV model with non-normal distributions can better fit futures data than the THSV model with the normal distribution. However, modeling the asymmetries alone within the standard THSV framework does not always produce better in-sample results than modeling non-normal properties within the SV framework. In addition, our estimation results provide strong evidence that there exist asymmetries in both returns and volatilities of all commodity futures under consideration, with a different degree of asymmetry across markets. Finally, we find that modeling both the mean and variance asymmetries and the fat-tailed feature in the return distributions is particularly important to accurately forecast one-day-ahead VaRs for long and short trading positions in Chinese commodity futures. More specifically, the volatility predictive ability of the THSV model with the mixture of normal distributions is the strongest for copper, natural rubber, and soybean futures, while the THSV model with generalized error distribution can better forecast future volatilities of aluminum futures. The remainder of this paper is organized as follows. Section 2 describes the THSV models with different distributions, and presents the Bayesian MCMC estimation and volatility forecasting and testing approaches. Section 3 discusses the data used in this analysis. Section 4 analyzes the asymmetric characteristics of futures returns based on the estimation results. Section 5 presents empirical results for out-of-sample VaR forecasts, while Section 6 concludes this paper.

This paper investigates the asymmetric characteristics in the mean and variance of Chinese commodity futures returns, using the THSV model with normal, student-t, generalized error, and mixture of normal distributions, respectively. The THSV approach enables us to examine asymmetries in the mean and variance dynamics simultaneously. To provide further insights into the ability of each model to forecast volatilities, the one-step-ahead VaRs for long and short trading positions are estimated and analyzed. Based on the DIC values, we show that the asymmetric THSV models can better describe the underlying mean and variance dynamics than the symmetric SV models for any given distribution assumption, regardless of the futures under consideration. We further demonstrate that the THSV model with fat-tailed distributions can better fit futures data than can the THSV model with the normal distribution. In particular, the THSV-MN outperforms other THSV alternative models for modeling 3 of 4 futures contracts considered. Our results also show that positive and negative shocks have asymmetric effects on the mean, variance, and variance autocorrelation of all commodity futures. However, the sizes of these asymmetric effects tend to vary across futures markets. In terms of the ability of forecasting one-day-ahead VaRs for long and short positions, we find that simply modeling fat-tailed properties with the symmetric SV model or modeling asymmetries in mean or variance alone does not help improve model performance over standard models. Modeling asymmetries in both mean and variance with an appropriate distribution assumption is crucial to accurately forecast VaRs for both long and short positions. In particular, the THSV-MN model is the best for copper, natural rubber, and soybean futures, while the THSV-GE model works best for aluminum futures in the Chinese markets.