Copula-based GARCH Models Research Articles

Portfolio value-at-risk estimation for spot chartering decisions under changing trade patterns: A copula approach.

Evolving geopolitical relationships between countries (especially between China and the United States) in recent years have highlighted dynamically changing trade patterns across the globe, all of which elevate risk and uncertainty for transport service providers. In order to mitigate risks, shipowners and operators must be able to estimate risks appropriately; one potentially promising method of doing so is through the value-at-risk (VaR) method. VaR describes the worst loss a portfolio is likely to sustain, which will not be exceeded over a target time horizon at a given level of confidence. This article proposes a copula-based GARCH model to estimate the joint multivariate distribution, which is a key component in VaR estimation. We show that the copula model can capture the VaR more successfully, as compared with the traditional method of calculation. As an empirical study, the expected portfolio VaR is examined when a shipowner chooses among Panamax soybean trading routes under a condition of reduced trade volumes between the United States and China due to the ongoing trade turmoil. This study serves as one of the very few papers in the literature on shipping portfolio VaR analysis. The results have significant implications for shipowners regarding fleet repositioning, decision making, and risk management.

The Dependence and Risk Spillover Between Energy Market and BRICS Stock Markets: A Copula-MGARCH Model Approach

The article examines the dynamic dependence structure and risk spillover between the future market of energy commodities and Brazil, Russia, India, China and South Africa (BRICS) stock markets for different market conditions. The study used copula-based multivariate GARCH model, or in short C-MGARCH model, to explore the conditional correlation by multivariate generalized autoregressive conditional heteroskedastic (MGARCH) and the remaining dependence by different copula models. Our results provide significant positive dynamic dependency among crude oil markets (natural gas market) and BRICS stock markets. We then explore the financial implications of volatility spillovers regarding portfolio risk management through an analysis of risk spillovers from energy market to BRICS countries using the value at Risk (VaR), conditional value at risk (CVaR) and delta CVaR. Our findings support the existence of significant risk spillover between crude oil markets (natural gas market) and BRICS stock markets. The presence of volatility spillover among oil prices, natural gas prices and BRICS stock market implies that oil market information (natural gas market information) enhances the volatility forecast in stock markets. Consequently, investors must take oil markets and natural gas markets into account at the time of financial portfolios structuring and in improving their hedging strategies.

On the sovereign debt crisis: sovereign credit default swaps and their interaction with stock market indices

ABSTRACT This paper examines the European credit default swap spreads and their relationship to other financial assets such as stock indices. This study aims at better investigating the European sovereign debt crisis from the beginning of 2010 to the end of 2013. For this purpose, using daily data covering the period from January 2004 to December 2018, first we examine the impact of the sovereign crisis on spread sovereign credit default swaps, using both an asymmetric DCC-MGARCH model and a Copula-based Multivariate GARCH model (C-MGARCH). Then, we estimate the relations between spread sovereign credit default swaps and equity indices. We analyse in particular the lead–lag relationship between these two financial indicators by using a vector autoregressive model. We note a negative correlation between the spreads and stock market indices. There is a significant unidirectional causality from CDS spread changes to stock market indices returns. Our findings show that the CDS spreads have played a leading role in most European countries during this crisis. These results are potentially important because the current pandemic is threatening the economies of European countries, especially Greece.

Is the role of precious metals as precious as they are? A vine copula and BiVaR approaches

This paper revisits the international evidence on hedge, safe haven, and diversification properties of precious metals—namelyW gold, silver, and platinum—for the G-7 stock markets. Therefore, this study proposes a multivariate vine copula-based GARCH model to assess the hedge and safe haven properties of precious metals and a Bivariate Value at Risk-based copula (BiVaR) measure to analyse the diversification potential of precious metals. Our empirical results suggest that; (1) gold is the strongest hedge and safe haven asset in almost all the G-7 stock markets, (2) silver and platinum results show that they may act as weak hedge assets, (3) silver bears the potential of a strong safe haven role only for Germany's and Italy's stock markets; however, platinum provides a weak safe haven role for most developed stock markets, (4) precious metals appear as interesting assets for diversifying a portfolio for G-7 stock markets investors. Overall, our findings provide noteworthy practical implication for investors.

Food Price Volatility and Asymmetries in Rural Areas of South Mediterranean Countries: A Copula-Based GARCH Model.

Many discussions following the 2007/08 food price crisis have revolved around the magnitude of the negative impacts that it may have had on food security worldwide. In South-Eastern Mediterranean countries (SEMC), food security is strongly interrelated with several key economic and political issues. Many of these countries are becoming increasingly import-dependent, particularly on cereals, which are the essential raw material for human and animal food and feed. Due to both their economic system structure and consumption, the SEMC are responsible for a third of world cereals imports, whereas they account for only 5% of the world population. Given the set of constraints and this dependence on global markets, SEMC will be probably more exposed to severe swings in agricultural commodity prices in the coming years. In this view, this study examines the dependence structure among global food grain markets and Morocco and provides flexible models for dependency and the conditional volatility GARCH. A copula-based GARCH model has been carried out to estimate the marginal distributions of Morocco and world cereals commodity price changes. The results revealed that the joint co-movement between agricultural commodity price changes around the world and in Morocco, are generally considerable and there exists asymmetric tail dependence.

Interdependence of oil prices and exchange rates: Evidence from copula-based GARCH model

This paper aims to investigate the conditional dependence structure between crude oil prices and three US dollar exchange rates (China, India and South Korea) from a new perspective using a copula-GARCH approach. Various kinds of copulas both time-invariant and time-varying dependence dynamics are fitted. Over the 2008–2018 period, the findings provide evidence of significant dependence in terms of symmetric structure between the oil prices and the exchange rate returns. Further, the tail dependence and dynamic dependence between two variables add a supplement to the explanatory ability of the model. Empirical results indicate the intercorrelation between crude oil and exchange rate movements, and provide benefits in risk diversification and inflation targeting. The findings also have significant implications for risk management, monetary policies to determine the behavior of fiscal policy in oil-exporting countries.

On the study of conditional dependence structure between oil, gold and USD exchange rates

Energy commodities and precious metals differ from other trading products. In fact, both oil and gold prices are leading economic variables and drive the evolution of the world economy. Since the US dollar is used as the primary currency of international crude oil and gold trading, the relationship between commodities, metals and exchange rates became a major research agenda recently. Therefore, this study proposes a Nested copula based GARCH models to explore the dependence structure between oil, gold and USD exchange rate. More importantly, a comparative framework based on three sub-periods is implemented to capture the co-movement during normal and crisis period. Empirical results suggest that for both crisis period the dependence between oil, gold and USD exchange rate is stronger comparing with the dependence during the untroubled period. Moreover, the co-movement is accelerated which is explained by the unusual movement of USD during the global financial crisis of 2007–2009.

Dynamic hedging with futures: a copula-based GARCH model with high-frequency data

Modeling the joint distribution of spot and futures returns is crucial for establishing optimal hedging strategies. This paper proposes a new class of dynamic copula-GARCH models that exploits information from high-frequency data for hedge ratio estimation. The copula theory facilitates constructing a flexible distribution; the inclusion of realized volatility measures constructed from high-frequency data enables copula forecasts to swiftly adapt to changing markets. By using data concerning equity index returns, the estimation results show that the inclusion of realized measures of volatility and correlation greatly enhances the explanatory power in the modeling. Moreover, the out-of-sample forecasting results show that the hedged portfolios constructed from the proposed model are superior to those constructed from the prevailing models in reducing the (estimated) conditional hedged portfolio variance. Finally, the economic gains from exploiting high-frequency data for estimating the hedge ratios are examined. It is found that hedgers obtain additional benefits by including high-frequency data in their hedging decisions; more risk-averse hedgers generate greater benefits.

Modeling Conditional Dependence of Stock Returns Using a Copula-based GARCH Model

Investigating dependence structures of stocks that are related to one another should be an important consideration in managing a stock portfolio, among other investment strategies. To capture various dependence features, we employ copula to overcome the limitations of traditional linear correlations. Financial time series data is typically characterized by volatility clustering of returns that influences an estimate of a stock’s future price. To deal with the volatility and dependence of stock returns, this paper provides procedures of combining a copula with a GARCH model which leads to the construction of a multivariate distribution. Using the copula-based GARCH approach that describes the tail dependences of stock returns, we carry out Monte Carlo simulations to predict a company’s movements in the stock market. The procedures are illustrated in two technology stocks, Apple and Samsung.

Conditional Dependence Structure between Oil, Gold and USD Exchange Rates: Nested Copula Based GARCH Model

Conditional Dependence Structure between Oil, Gold and USD Exchange Rates: Nested Copula Based GARCH Model

Dependency between Risks and the Insurer’s Economic Capital: A Copula-based GARCH Model

Abstract Copulas can be a useful tool to capture heavy-tailed dependence between risks in estimating economic capital. This paper provides a procedure of combining copula with GARCH model to construct a multivariate distribution. The copula-based GARCH model using a skewed student’s t-distribution controls for the issues of skewness, heavy tails, volatility clustering and conditional dependencies contained in the financial time series data. Using the sample of U.S. property liability insurance industry, we perform Monte Carlo simulation to estimate the insurer’s economic capital measured by Value-at-Risk (VaR) and Expected Shortfall (ES). The result indicates that the choice of dependence structure and business mix between asset classes and liability lines has a significant impact on the resulting capital requirements and diversification benefits. We find the incremental diversification benefit in terms of a reduction in the total capital requirement from the joint modeling of underwriting risk and market risk compared to the modeling of market risk only.

Optimal gasoline hedging strategies using futures contracts and exchange-traded funds

This article employs a variety of econometric models (including OLS, VEC/VAR, DCC GARCH and a class of copula-based GARCH models) to estimate optimal hedge ratios for gasoline spot prices using gasoline exchange-traded funds (ETFs) and gasoline futures contracts. We then compare their performance using four different measures from the perspective of both their hedging objectives and trading position using four different measures: variance reduction measure, utility-based measure and two tail-based measures (value at risk and expected shortfall). The impact of the 2008 financial market crisis on hedging performance is also investigated. Our findings indicate that, in terms of variance reduction, the static models (OLS and VEC/VAR) are found to be the best hedging strategies. However, more sophisticated time-varying hedging strategies could outperform the static hedging models when the other measures are used. In addition, ETF hedging is a more effective hedging strategy than futures hedging during the high-volatility (crisis) period, but this is not always the case during the normal time (post-crisis) period.

Modelling dependence between tourism demand and exchange rate using the copula-based GARCH model

This paper investigates dependence between tourism demand and exchange rate, using the case of China, and from a new perspective by using copula–GARCH models. The empirical results show that the volatility of exchange rate is not a determinant factor in fluctuation of China's inbound tourism demand from the countries being studied. Furthermore, only Russia exhibits risk-adverse behaviour with extreme SUR depreciation, or CNY appreciation associated with an extreme decline in arrivals. Third, introducing the tail dependence and dynamic dependence between growth rates of tourism demand and exchange rate add much to the explanatory ability of the model. The findings of this study have important implications for destination manager and travel agent as it helps to understand the impact of exchange rates on China inbound tourism demand and provide a complementary academic approach on evaluating the role of exchange rates in the international tourism demand model.

Modeling volatility and dependency of agricultural price and production indices of Thailand: Static versus time-varying copulas

Volatility and dependence structure are two main sources of uncertainty in many economic issues, such as exchange rates, future prices and agricultural product prices etc. who fully embody uncertainty among relationship and variation. This paper aims at estimating the dependency between the percentage changes of the agricultural price and agricultural production indices of Thailand and also their conditional volatilities using copula-based GARCH models. The motivation of this paper is twofold. First, the strategic department of agriculture of Thailand would like to have reliable empirical models for the dependency and volatilities for use in policy strategy. Second, this paper provides less restrictive models for dependency and the conditional volatility GARCH. The copula-based multivariate analysis used in this paper nested the traditional multivariate as a special case (Tae-Hwy and Xiangdong, 2009) [13]. Appropriate marginal distributions for both, the percentage changes of the agricultural price and agricultural production indices were selected for their estimation. Static as well as time varying copulas were estimated. The empirical results were found that the suitable margins were skew t distribution and the time varying copula i.e., the time varying rotate Joe copula (270°) was the choice for the policy makers to follow. The one-period ahead forecasted-growth rate of agricultural price index conditional on growth rate of agricultural production index was also provided as an example of forecasting it using the resulted margins and time-varying copula based GARCH model.

An economic evaluation of stock–bond return comovements with copula-based GARCH models

Owing to their importance in asset allocation strategies, the comovements between the stock and bond markets have become an increasingly popular issue in financial economics. Moreover, the copula theory can be utilized to construct a flexible joint distribution that allows for skewness in the distribution of asset returns as well as asymmetry in the dependence structure between asset returns. Therefore, this paper proposes three classes of copula-based GARCH models to describe the time-varying dependence structure of stock–bond returns, and then examines the economic value of copula-based GARCH models in the asset allocation strategy. We compare their out-of-sample performance with other models, including the passive, the constant conditional correlation (CCC) GARCH and the dynamic conditional correlation (DCC) GARCH models. From the empirical results, we find that a dynamic strategy based on the GJR-GARCH model with Student-t copula yields larger economic gains than passive and other dynamic strategies. Moreover, a less risk-averse investor will pay higher performance fees to switch from a passive strategy to a dynamic strategy based on copula-based GARCH models.

The economic value of co-movement between oil price and exchange rate using copula-based GARCH models

The US dollar is used as the primary currency of international crude oil trading; as such, the recent substantial depreciation in the US dollar has resulted in a corresponding increase in crude oil prices. In addition, oil price and exchange-rate returns have been shown to be skewed and leptokurtic, and to exhibit an asymmetric or tail dependence structure. Therefore, this study proposes dynamic copula-based GARCH models to explore the dependence structure between the oil price and the US dollar exchange rate. More importantly, an asset-allocation strategy is implemented to evaluate economic value and confirm the efficiency of the copula-based GARCH models. In terms of out-of-sample forecasting performance, a dynamic strategy based on the CGARCH model with the Student-t copula exhibits greater economic benefits than static and other dynamic strategies. In addition, the positive feedback trading activities are statistically significant within the oil market, but this information does not enhance the economic benefits from the perspective of an asset-allocation decision. Finally, a more risk-averse investor generates a higher fee for switching from a static strategy to a dynamic strategy based on copula-based GARCH models.

Copula-based multivariate GARCH model with uncorrelated dependent errors

Abstract Multivariate GARCH (MGARCH) models are usually estimated under multivariate normality. In this paper, for non-elliptically distributed financial returns, we propose copula-based multivariate GARCH (C-MGARCH) model with uncorrelated dependent errors, which are generated through a linear combination of dependent random variables. The dependence structure is controlled by a copula function. Our new C-MGARCH model nests a conventional MGARCH model as a special case. The aim of this paper is to model MGARCH for non-normal multivariate distributions using copulas. We model the conditional correlation (by MGARCH) and the remaining dependence (by a copula) separately and simultaneously. We apply this idea to three MGARCH models, namely, the dynamic conditional correlation (DCC) model of Engle [Engle, R.F., 2002. Dynamic conditional correlation: A simple class of multivariate generalized autoregressive conditional heteroskedasticity models. Journal of Business and Economic Statistics 20, 339–350], the varying correlation (VC) model of Tse and Tsui [Tse, Y.K., Tsui, A.K., 2002. A multivariate generalized autoregressive conditional heteroscedasticity model with time-varying correlations. Journal of Business and Economic Statistics 20, 351–362], and the BEKK model of Engle and Kroner [Engle, R.F., Kroner, K.F., 1995. Multivariate simultaneous generalized ARCH. Econometric Theory 11, 122–150]. Empirical analysis with three foreign exchange rates indicates that the C-MGARCH models outperform DCC, VC, and BEKK in terms of in-sample model selection and out-of-sample multivariate density forecast, and in terms of these criteria the choice of copula functions is more important than the choice of the volatility models.