The time-varying and asymmetric dependence between crude oil spot and futures markets: Evidence from the Mixture copula-based ARJI–GARCH model

This paper designs a Mixture copula-based ARJI–GARCH model to simultaneously investigate the dynamic process of crude oil spot and futures returns and the time-varying and asymmetric dependence between spot and futures returns. The individual behavior of each market is modeled by the ARJI–GARCH process. The time-varying and asymmetric dependence is captured by the Mixture copula which is composed of the Gumbel copula and Clayton copula. Empirical results show three important findings. First, jumping behavior is an important process for each market. Second, spot and futures returns do not have the same jump process. Third, the tail dependence between spot and futures markets is time-varying and asymmetric with the magnitude of upper tail dependence being slightly weaker than that of lower tail dependence.     

Modeling hedge fund exposure to risk factors

This paper examines the adjustment dynamics of hedge fund returns and studies their exposure to risk factors in a nonlinear framework for several types of strategies over the last two decades. Nonlinearity is justified by distortions due to the use of short selling, leverage, derivatives and illiquid assets for hedge fund strategies. Among nonlinear models, switching regime (STR) models are applied to reproduce the dynamics of hedge fund returns. This nonlinear multivariate modeling has the advantage of capturing the time-varying exposure of hedge fund strategies to risk factors, and of specifying the asymmetric relationship between hedge fund returns and risk. The findings are interesting and provide several contributions to the hedge fund literature. First, we show that the dynamics of hedge fund returns exhibit significant asymmetry and nonlinearity, indicating that they evolve and vary asymmetrically in accordance with stages in financial cycles. Second, hedge fund exposure to risk factors also varies over time, depending on the strategy and the regime. Finally, our modeling captures the most important changes in hedge fund exposure to risk factors induced by the recent global financial crisis (2008–2009).     

股票资产组合VaR研究基于混合D藤Copula模型

本文在对上证市场五种股票资产组合的风险分析中以VaR作为风险度量指标,采用基于Pair Copula高维建模理论的混合D藤Copula模型,建立了反应多个资产组合相关结构的联合分布模型。该模型对传统D藤Copula建模方法作了进一步的改进,通过一定的选择标准,确定了D藤中每个Pair Copula函数的最优函数族,这样使得所建立的模型不仅考虑到了资产维数的影响,而且还能捕捉到组合内部因子间相关结构的差异性,从而改进后的模型能更好地描述资产组合的相关结构,并且能更精确地反映资产组合收益的实际分布。最后,以混合D藤Copula模型为基础,利用Monte Carlo方法计算了上证市场五种股票资产组合的VaR,并通过实证研究进一步证明了该模型的有效性。     

Estimating value-at-risk under a Heath–Jarrow–Morton framework with jump

This article proposes a new methodology for measuring Value-at-Risk (hereafter VaR) using a model that incorporates both volatility and jumps. Heath–Jarrow–Morton (HJM) model has been used for the valuation of interest rate derivatives. This study extends the use of HJM model to the estimation VaR. This article specifically uses a two-factor HJM jump-diffusion model for the computation. The study models the Eurodollar futures prices using its derivatives. In addition, this article uses a new volatility specification of Ze-To (2002) to construct the HJM dynamics. The result indicates that the VaR model using HJM jump-diffusion framework performs well in capturing the nonnormality and in providing accurate VaR forecasts in the in-sample and out-sample tests.     

Market volatility and the dynamic hedging of multi-commodity price risk

Commodity cash and futures prices experienced a severe boom-and-bust cycle between 2006 and 2009. Increases in commodity price volatility have raised concerns about the usefulness of commodity futures and options as risk management tools. Dynamic hedging strategies have the potential to improve risk management when conditional (co)variances depart significantly from their unconditional, long-run counterparts and may be useful to decision-makers despite their greater complexity and higher transaction costs. We propose a Nonparametric Copula-based Generalized Autoregressive Conditional Heteroscedastic (NPC-GARCH) approach to estimate time-varying hedge ratios, and evaluate the benefits of dynamic hedging during four sub-periods between 2000 and 2011 using a stylized Texas cattle feedlot management problem. The NPC-GARCH approach allows for a flexible, nonlinear and asymmetric dependence structure between cash and futures prices for different commodities. We find that NPC-GARCH dynamic hedging performs better than either static, GARCH-Dynamic Conditional Correlation (DCC) or GARCH-Baba, Engle, Kraft and Kroner (BEKK) hedging in terms of lower tail risk (expected shortfall), but that there is no significant difference between hedging approaches in terms of portfolio variance reduction.     

The macroeconomic drivers in hedge fund beta management

We investigate how macroeconomic indicators alter the dynamic risk exposure of different hedge fund style strategies. We implement a multifactor model to estimate the unobservable time-varying risk exposure conditional on macroeconomic information and a VAR to measure the impact of macroeconomic predictors on different time horizons. Using monthly returns on a cross-section of 10 different style indices from February 1997 to August 2019, we find that, on average, macroeconomic indicators explain approximately 30%, 55%, and 75% of the variability of betas at 1-, 6-, and 36-month horizons, respectively. Although macroeconomic predictors play a critical role at every horizon, at 1 month, the dominating effect comes from idiosyncratic shocks, which indicates that in the short run, hedge fund managers rely mostly on their own reallocation signals. Moreover, consistent with the fundamental drivers of the smart beta factors, we find that the interest rate level and GDP growth similarly impact hedge fund exposures across styles.     

Modelling the volatility of the tanker freight market based on improved empirical mode decomposition

In this article, a method based on empirical mode decomposition (EMD) and BEKK–Multivariate GARCH (MVGARCH) is developed to analyse the volatility of the tanker freight market. First, the initial time series of tanker freight rates is decomposed into several independent intrinsic mode functions (IMFs). Next, the IMFs are composed as three components by an improved EMD: the long-term trend time series that represents the benchmark freight rates of the tanker freight market, the high-frequency time series that reflects the short-term supply–demand relation and the low-frequency time series caused by extreme events. Based on the results of EMD, the volatility spillover effects between the freight rates of Aframax, Suezmax and Very Large Crude Carrier (VLCC) markets are tested by the BEKK–MVGARCH model. The results indicate that there are volatility spillover effects between the reconstructed components, although the volatility spillover effects between the original freight series are not significant. The improved EMD method contributes to the retention of the economic characteristics of the original time series, thereby providing a vital approach for tanker freight market analysis. Furthermore, the potential volatility spillover among different sub-markets can be investigated through the integration of EMD and the BEKK–MVGARCH.     

A range-based volatility approach to measuring volatility contagion in securitized real estate markets

We use a newly-developed time-varying range-based volatility model to capture the dynamics of securitized real estate volatility. The novelty of the model is the use of a smooth transition copula function to capture the nonlinear comovements between major REIT markets in the presence of structural changes. We then investigate the impact of extreme events on the volatility dependence in a broad set of 13 developed countries over the period from 1990 to 2012. We find that information transmission through the volatility channel can exhibit either bi- or uni-directional causality. In addition, financial contagion following the subprime crisis is found between the U.S. and Australia.     

Energy portfolio risk management using time-varying extreme value copula methods

This work is concerned with the statistical modeling of the dependence structure between three energy commodity markets (WTI crude oil, natural gas and heating oil) using the concept of copulas and proposes a method for estimating the Value at risk (VaR) of energy portfolio based on the combination of time series models with models of the extreme value theory before fitting a copula. Each return series is modeled by AR-(FI) GARCH univariate model. Then, we fit the GPD distribution to the tails of the residuals to model marginal residuals distributions. The extreme value copula to the iid residuals is fitted and we simulate from it to construct N portfolios and estimate VaR. As a first step, the method is applied to a two-dimensional energy portfolio. In second step, we extend method in trivariate context to measure VaR of three-dimensional energy portfolio. Dependences between residuals are modeled using a trivariate nested Gumbel copulas. Methods proposed are compared with various univariate and multivariate conventional VaR methods. The reported results demonstrate that GARCH-t, conditional EVT and FIGARCH extreme value copula methods produce acceptable estimates of risk both for standard and more extreme VaR quantiles. Generally, copula methods are less accurate compared with their predictive performances in the case of portfolio composed of exchange market indices.     

Forecasting spot freight rates based on forward freight agreement and time charter contract

In this article, the lead–lag relationship in freight rates between spot and forward markets and between spot and time charter (TC) markets was investigated. A hybrid forecasting method for spot freight rates was proposed based on the price discovery functions of the freight forward agreement (FFA) and the TC contract. VECM-based models were developed to analyse the relation between spot rates and FFA and TC rates. Empirical results indicate that cointegration does exist between spot and FFA rates and between spot and TC rates. Furthermore, while both FFA and TC rates are helpful in forecasting spot freight rates, the integration of the two can further improve the forecasting performance of spot freight rates.     

Value at risk estimation by threshold stochastic volatility model

This article proposes a threshold stochastic volatility model that generates volatility forecasts specifically designed for value at risk (VaR) estimation. The method incorporates extreme downside shocks by modelling left-tail returns separately from other returns. Left-tail returns are generated with a t-distributional process based on the historically observed conditional excess kurtosis. This specification allows VaR estimates to be generated with extreme downside impacts, yet remains empirically widely applicable. This article applies the model to daily returns of seven major stock indices over a 22-year period and compares its forecasts to those of several other forecasting methods. Based on back-testing outcomes and likelihood ratio tests, the new model provides reliable estimates and outperforms others.     

Dynamic multiproduct optimal hedging in the soybean complex – do time-varying correlations provide hedging improvements?

Optimal multiproduct time-varying hedge ratios are determined – for a soybean complex – and their risk-mitigating impact is contrasted over single-commodity time-varying and naive hedge ratios. A parsimonious regime-switching dynamic correlation model is employed, with the estimated dynamic correlation matrix among prices varying between two different levels, and the time-varying correlations being applied to the multiproduct setting. Findings obtained are three-fold. First, there is significant evidence that estimated simultaneous correlations among different commodities’ prices (e.g. soybean spot and soybean meal futures) attain different values along the time series. Second, there is a substantial reduction in margin variance provided by the optimal multiproduct time-varying hedge ratios over single time-varying and naive hedge ratios, for both in- and out-of-sample data. Third, average optimal multiproduct time-varying hedge ratios for soybean and soybean meal (0.82 and 0.74, respectively; for out-of-sample data) are significantly below the naive full hedge ratio, providing risk mitigation at lower costs.     

中国公司债券交易量与价格波动的关系

使用中国沪深证券交易所的公司债数据,检验了债券交易量与价格波动的线性关系和非线性尾部相关性,分析了债券流动性水平对量价关系的影响,研究了债券量价关系的时变特征。结果表明:中国公司债市场中债券交易量与价格波动之间存在显著的线性关系;债券流动性水平对量价关系有显著影响,债券流动性水平越高(低),则量价关系越弱(强);债券交易量与价格波动存在非对称的下尾相关性;债券量价关系具有时变性,市场低风险时期量价关系较弱,市场高风险时期量价关系较强。     

Testing the Gaussian and Student's t copulas in a risk management framework

This paper introduces a semiparametric framework for selecting either a Gaussian or a Student's t copula in a d-dimensional setting. We compare the two models using four different approaches: (i) four goodness-of-fit graphical plots, (ii) a bootstrapped correlation matrix generated in each scenario with the empirical correlation matrix used as a benchmark, (iii) Value-at-Risk (VaR) and Expected Shortfall (ES) as risk measures, and (iv) co-Value-at-Risk (CoVaR) and Marginal Expected Shortfall (MES) as co-risk measures. We illustrate this four-step procedure using a portfolio of daily returns of six international stock indices. The VaR results confirm that the t-based copula model is an attractive alternative to the Gaussian. The ES analysis is less conclusive, and indicates that risk managers should jointly use the risk measure as well as the copula model. The results highlight the importance of promoting stress testing rather than ES in the risk management industry, particularly in the aftermath of a financial crisis.     

石化权证在GARCH模型下的实证检验

股票价格的波动率特征是股票衍生品价格的决定性因素。Black&Scholes假设股票价格服从几何布朗运动,其重要的假设条件是波动率为一个常数。但是,越来越多的实证研究结果表明,股票收益率存在显著的尖峰厚尾现象,其波动率存在明显的时变性特征。因此,放宽波动率恒定条件,并且研究股票波动率的变动特征,对认购权证的正确定价具有重要意义。     

Is the cryptocurrency market a hedge against stock market risk? A Wavelet and GARCH approach

This study analyses six major cryptocurrencies and four global stock markets to explore the role of cryptocurrencies as a hedge, safe haven, and diversifier in stock markets. The study employs ADCC-GARCH and Wavelet Coherence Technique, using daily data from 4 January 2017 to 28 February 2023. The study has found that stock returns and unstable cryptocurrency returns have high volatility persistence in the long run. Besides, while unstable digital currencies (Bitcoin, Ethereum, Binance Coin, and Dogecoin) serve as a hedge during stable economic periods, they have not been a hedge during economic turmoil in the stock markets. Conversely, stablecoins (Tether and USD Coin) have been shown to have acted as a hedge during normal economic times and have offered a safe haven during economic downturns. Except for Tether, all cryptocurrencies' diversification capacity is time-varying. In stable economic conditions, they serve as diversifiers, but during turmoil, they do not. However, Tether serves as a diversifier regardless of the financial situation. Finally, the present investigation is expected to offer crucial information on hedge, safe haven and diversification for quasi-investors.     

Identifying the dynamic relationship between tanker freight rates and oil prices: In the perspective of multiscale relevance

The tanker shipping market has been treated as the key extension of the world oil market and inevitably, its uncertainty is correlated to volatility of the oil market, besides supply and demand factors. Therefore, for improving operational management and budget planning decisions, it is essential to understand the inherent relevance between freight rates and crude oil prices. Taking time-dependent features into account, this paper focuses on the multiscale correlation between freight rates and oil prices. Given the complexity and mutability of tanker freight rate process, this paper first extracts the intrinsic mode functions from the original data using the Ensemble Empirical Mode Decomposition model and then reconstructs two separate composite functions: high-frequency and low-frequency components, plus the residual as the long-term trend. Secondly, correlations of the multiscale components of freight rates and oil prices are examined based on relevance structure. Empirical results show that tanker freight rates and oil prices exhibit different multiscale properties with true economic meaning and are significantly correlated in the medium and the long term when taking the relevance structure into account. These findings offer some useful information to better understand the correlations between these two markets and more importantly, propose a novel perspective to investigate the dynamic relationship between two markets.     

Modeling the volatility of futures return in rubber and oil—A Copula-based GARCH model approach

This paper attempts to make use of a Copula-based GARCH (Generalized AutoRegressive Conditional Heteroskedasticity) Model to find out the relationships between the volatility of rubber futures returns in the Agricultural Futures Exchange of Thailand (AFET) and other four main markets, namely, the volatility of rubber futures returns in the Singapore Commodity Exchange (SICOM), the volatility of rubber futures returns, crude oil returns, and gas oil returns in the Tokyo Commodity Exchange (TOCOM). The results illustrate that the Student-t dependence only shows better explanatory power than the Gaussian dependence structure and the persistence pertaining to the dependence structure between rubber futures returns in AFET and oil futures returns, namely, crude oil futures returns and gas oil futures returns in TOCOM. Whereas, the Gaussian dependence shows better explanatory ability between rubber futures returns in AFET and other rubber futures returns, namely, the volatility of rubber futures in SICOM and TOCOM. For the multivariate Copula model, all the parameters between AFET and other variables are significant. Based on these results, with the liberalization of agricultural trade and the withdrawal of government support to agricultural producers, there is in many countries a new need for price discovery and even physical trading mechanisms, a need that can often be met by commodity futures exchanges. Hence, this paper recommends that the government supports the hedge mutual funds that can be invested in every commodities futures exchange in the world. It can also put the funds together that will contribute farmers to invest in each commodities futures market.     

Risk premia in forward foreign exchange rates: a comparison of signal extraction and regression methods

We investigate possible presence of time-varying risk premia in forward pound, yen, and Euro monthly exchange rates versus the US dollar over the last two decades. We study this issue using regression techniques and separately using a signal plus noise model. Our models account for time-varying volatility and non-normality in the observed series. Our regression model rejects the hypothesis that the forward rate is an unbiased predictor of future spot exchange rate, indicating the existence of time-varying risk premium under rational expectations. Our signal plus noise model reveals a time-varying risk premium component in yen and Euro. The same model provides evidence for the presence of risk premium in pound over a shorter sample period, though not over the entire sample. We conclude that risk premia exist, although we may fail to detect these for some currencies over specific time periods.     

最小平均VaR套期保值比率计算模型及实证研究

针对传统的套期保值模型只考虑最小化套期保值组合在到期日的价格风险,而且没有充分利用资产历史价格样本数据所提供的收益率信息的特点,本文提出了考虑套期保值期内不同期限价格风险的最小平均VaR套期保值比率计算模型。基于我国外汇市场及股票市场数据,本文对最小平均VaR套期保值模型进行了实证分析,并与常用的最小方差及最小VaR套期保值模型进行了对比,得出了最小平均VaR模型在套期保值过程中的效果要优于其他两种模型,能更有效地降低投资者提前终止套期保值可能面临额外风险的结论。