پیش بینی نوسانات و مدیریت ریسک برای بازار کالا با حضور عدم تقارن و حافظه بلند مدت

This paper explores the relevance of asymmetry and long memory in modeling and forecasting the conditional volatility and market risk of four widely traded commodities (crude oil, natural gas, gold, and silver). A broad set of the most popular linear and nonlinear GARCH-type models is used to investigate this relevancy. Our in-sample and out-of-sample results show that volatility of commodity returns can be better described by nonlinear volatility models accommodating the long memory and asymmetry features. In particular, the FIAPARCH model is found to be the best suited for estimating the VaR forecasts for both short and long trading positions. This model also gives for all four commodities the lowest number of violations under the Basel II Accord rule, given a risk exposure at the 99% confidence level. Several implications for commodity market risks, policy regulations and hedging strategies can be drawn from the obtained results.

The literature on commodities has concentrated mainly on price co-movements and information transmission between returns. On the other hand, the research on conditional commodity return volatility and market risk has been less generous than the counterpart on commodity prices and returns. However, studies focusing on commodity volatility have been gaining importance due to rising volatility and the increasing role commodities play in the international asset markets (e.g., Creti et al., 2013, Dahl and Iglesias, 2009, Kang and Yoon, 2013, Regnier, 2007, Thuraisamy et al., 2013 and Vivian and Wohar, 2012). The increased interest is also due to the fact that commodity returns possess empirical stylized characteristics such as non-normal distribution, asymmetry, structural breaks and fat tails that affect model performance (e.g., Aloui and Mabrouk, 2010, Cheng and Hung, 2011, Cheong, 2009 and Hung et al., 2008), and thereby require experimentation with different volatility models. The traditional strand of research on commodity volatility largely addresses dynamic volatility behavior of a single commodity or volatility transmission across several commodities over time, using the standard volatility models. New studies however attempt to accommodate the varying characteristics of volatility of a commodity or a group of commodities in order to come up with a methodological representation that forecasts future volatility of a single commodity or a portfolio more accurately (e.g., Arouri et al., 2012a, Arouri et al., 2012b and Wei et al., 2010). The research on commodity market risks often uses the value-at-risk (VaR) approach based on the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) family models to evaluate the validity and forecasts of volatility models. A model is said to be best suited for modeling the conditional volatility of commodity markets if it provides the most accurate VaR estimates and forecasts. Since the dust has not been settled and the jury is still out on the suitability of volatility models to model commodity volatility behavior, this article will therefore evaluate the accuracy of various linear and nonlinear models using, in addition to the VaR approach, different evaluation and forecasting criteria. Moreover, there are actually only a few studies that examine the choice between volatility models for commodities markets despite the increasing financialization and volatility of these markets, and they often fall short of adequately characterizing volatility behavior. 1 The results from this research are of great interest for various economic agents including international investors, energy managers, and policymakers who constantly seek to better understand the volatility dynamics of commodity prices in order to build efficient risk-hedging models as well as to implement sound policies to heed inflation pressure. More concretely, our first objective is to examine the suitability of GARCH-class models in modeling conditional volatility and market risk (VaR) of four most widely traded commodities (crude oil, natural gas, gold and silver) in the presence of long memory and asymmetric effects. Moreover, these commodities have impacts on real economic activity, financial markets, and financial, economic and geopolitical risks. The importance of the long memory and asymmetry properties has been demonstrated not only for modeling the volatility of commodity volatility but also for improving the accuracy of VaR estimates and forecasts (e.g., Aloui and Mabrouk, 2010, Cheong, 2009 and Wei et al., 2010). Our second objective is to compare the out-of-sample predictive performance of competing GARCH models based on commonly-used evaluation criteria and the VaR approach for both portfolio short and long positions. Furthermore, we evaluate the economic importance of our results by computing the Basel II Accord's daily capital requirements for individual commodities, given the VaR estimates derived from competing GARCH models. In comparison with existing studies on volatility forecasting, we consider a broader set of GARCH-type models which includes four linear specifications (GARCH, EGARCH, IGARCH, and RiskMetrics) and three nonlinear specifications (FIGARCH, FIAPARCH and HYGARCH). In comparison with previous studies, our dataset is extended to cover the spot and futures prices of natural gas, gold and silver, in addition to the frequently studied spot and futures price of crude oil (e.g., Agnolucci, 2009, Arouri et al., 2012b, Kang et al., 2009, Sadorsky, 2006 and Wei et al., 2010). The choice of these four major commodities (crude oil, natural gas, gold, and silver) is motivated by the fact that they altogether represent the strategic commodities that have significant influences on the real sector, financial sector, and economic growth of national economy (e.g., Browne and Cronin, 2010, Cologni and Manera, 2009, Hamilton, 1996 and Holmes and Wang, 2003). Moreover, while past studies have extensively investigated the issue of volatility modeling and forecasting for crude oil and related petroleum products ( Arouri et al., 2012b and Wei et al., 2010; and references therein), none of them have extended their samples to include natural gas, gold, and silver at the same time in order to get a comparative view of volatility behavior across these different types of commodities. For instance, Baur and McDermott (2010) provide evidence that gold is both a hedge and a safe haven for major European stock markets and the US but not for Australia, Canada, Japan and large emerging markets such as the BRIC countries. Arouri et al. (2012a) investigate the potential of structural change and long memory (LM) properties in returns and volatility of the four major precious metals traded on the COMEX markets (gold, silver, platinum, and palladium) and show evidence that conditional volatility of precious metals is better explained by long memory than by structural breaks. The paper distinguishes itself from the literature in several ways. The recent literature that deals with commodity markets separates asymmetry from long memory and concentrates more on the former than the latter. Our paper combines both statistical properties for these widely traded commodities, including natural gas which is not researched in the literature as much as crude oil and its refined products are. Moreover, the past research on volatility forecasting for commodity markets is limited as it has focused more on forecasting conditional return than conditional volatility. Our paper conducts conditional volatility forecasts in the presence of asymmetry and dual long memory. It also seeks to find the best suited model for estimating the VaR forecasts for both short and long trading positions. Finally, it examines the lowest number of violations under the Basel II Accord rule for the four commodities. Overall, the main contributions of this study are the following: (1) over the in-sample period, the FIAPARCH is the best suited model in almost all cases, while the standard GARCH model is selected only once; (2) none of the competing models absolutely outperforms the others in terms of volatility forecasts, but the nonlinear GARCH models perform better than the linear models, regardless of the forecasting horizons; and (3) the FIAPARCH provides the best VaR estimates and forecasts for all commodities at almost all confidence levels. This model also leads to the lowest number of violations (i.e., number of times that actual losses exceed VaR estimates). The foremost implications of our findings have strong bearing to volatility model building for commodity markets. On the other hand, large violations under the Basel II Accord may lead to failures of financial institutions that invest in commodities, as the capital requirements implied by the VaR threshold forecasts may be insufficient to cover the realized losses. Lower than ten violations imply that these models do not lead to entry in the red zone which is important for an institutions' image, reputation, and risk management. The remainder of the article is structured as follows. Section 2 reviews the major studies focusing on modeling and forecasting of commodity volatility. Section 3 presents the econometric approach. Section 4 describes the data used, while Section 5 reports and discusses the empirical results. The concluding remarks are provided in Section 6.

This article examines the relevance and usefulness of long memory and asymmetry in modeling and forecasting the conditional volatility and market risk for the four most widely traded commodities – oil, natural gas, gold and silver. By adopting the GARCH-typemethodology, our empirical framework allows to not only identify the best volatility model as it has been done in several past studies (e.g., Cheong, 2009; Kang et al., 2009), but also to investigate the ability of competing GARCH-type models to forecast the market risk (the VaR) associated with commodity markets as well as their suitability for the determination of daily capital charges of financial institutions under the Basel II Accord. In contrast to existing studies, our sample is extended to also cover the spot and futures prices of the four commodities, and we also consider a broader set of seven linear and nonlinear GARCH-type models (GARCH, IGARCH, EGARCH, RiskMetrics, FIGARCH, FIAPARCH and HYGARCH). Regarding the empirical results, we find that no single GARCH-type model absolutely outperforms the others over both the in-sample and out-of-sample periods, even though nonlinear GARCH models, particularly the EGARCH and FIAPARCHmodels, achieve superior performance to linear GARCHmodels. Interestingly, our in-sample and out-of-sample VaR estimations show that the FIAPARCH provides better forecasting accuracy than do the next bestmodels (GARCH and EGARCH) identified by the volatility forecast analysis. Thus, not only the long memory but also the asymmetric effects are important for modeling and forecasting the conditional volatility of the commodities we studied. The correct choice of a GARCH-type specification appears to be a challenging task. This challenge should give better opportunities for more active arbitrage in the commoditymarkets and requiremarket participants to check the relevance of a particular GARCH-typemodel before making use of it. To some extent, our results support the Basel Accord's tolerance for financial institutions to build their own models to forecast the VaR as none of our empirical GARCHmodels outperforms the others in terms of both the percentage of violations and capital requirements. Financial institutions should, however, prefer the FIAPARCH model as it produces the lowest number of violations for all the commodities considered. The relevant models show evidence of asymmetry in the four commodity markets. This implies that model builders should favor models that cater for asymmetry when they examine commodity markets. Accordingly, policymakers should be aware that negative shocks such as recessions, wars and surges in geopolitical risk have stronger effects on conditional volatility than positive shocks such as new discoveries or improvement in the economy, with the exception of gold as explained below. The relevant models also show that the commodity markets are characterized by longmemory which suggests that models like FIGARCH, FIAPARCH and HYGARCH are preferred to those like GARCH and IGARCH. The results also show that the precious metals, gold and silver, are different from crude and oil when it comes to modeling returns and asymmetry. We find evidence of a significant return predictability for futures returns in case of the FIAPARCH model and the case is stronger for silver than gold. This implies lower persistence and faster meanreversion in gold and silver returns, and more suitability in using the FIAPARCH model over the family of the GARCH models. Interestingly, we document that the impact of positive shocks on conditional volatility is greater than that of negative shocks.