copula-GARCH Model Research Articles

Marginals versus copulas: Which account for more model risk in multivariate risk forecasting?

We study the model risk of multivariate risk models in a comprehensive empirical study on Copula-GARCH models used for forecasting Value-at-Risk and Expected Shortfall. To determine whether model risk inherent in the forecasting of portfolio risk is caused by the candidate marginal or copula models, we analyze different groups of models in which we fix either the marginals, the copula, or neither. Model risk is economically significant, especially high during periods of crisis, and almost completely due to the choice of the copula. We then propose the use of the model confidence set procedure to narrow down the set of available models and reduce model risk for Copula-GARCH risk models. Our proposed approach leads to a significant reduction of the model risk of one day ahead forecasts by our various candidate risk models.

A changepoint analysis of exchange rate and commodity price risks for Latin American stock markets

Focusing on countries whose economies are exposed to fluctuations in commodity prices and exchange rates, we study the vulnerability of these stock market returns to exchange rate and commodity price shocks using non-parametric structural break tests for volatility and dependence. The return distributions are modeled using a Copula-GARCH model incorporating the estimated changepoints and we measure risk-spillovers with the conditional Value-at-Risk. We find evidence for various changepoints at different points in time, implying changes in risk and spillovers. In particular, there is evidence of increased spillover risk after the outbreak of the global financial crisis in 2008, as well as higher conditional risk following the Covid-19 outbreak.

Volatility and tail dependence between sustainable stock indices during the COVID-19 pandemic

Motivation: The motivation behind the study was to analyze the risk of sustainable stock indices (SSIs) and their conventional peers during the COVID-19 health crisis. We wanted to check if SSIs were more resistant to market risk in the times of huge volatility as well as what the correlation between particular SSIs was and, similarly, between their conventional peers. Aim: The main objective of the study was to analyze volatility spillover among sustainability stock indices (SSIs) and their conventional peers during the COVID-19 health crisis. The authors analyze conditional volatility among SSIs, which was obtained from univariate GARCH-type models, and the tail dependence coefficient, which was derived from the Copula-GARCH models. The indices from FTSE4Good family for the USA, Europe and Japan markets together with their corresponding conventional indices have been chosen. Results: The research shows that during the COVID-19 health crisis SSIs were less volatile than their conventional peers. Moreover the relations between particular SSIs in most cases were weaker, whereas extreme observations which occurred were less concordant for conventional indices. It implies that the stability of sustainable stock indices from FTSE4good family is greater than for their conventional peers.

The application of the hybrid copula-GARCH approach in the simulation of extreme discharge values

Statistical analysis and simulation of annual maximum discharge values, while considering the corresponding maximum daily rainfall, provide a comprehensive view of flood management. This research presents the application of copula functions for simulating and modeling two variables of annual maximum discharge and corresponding precipitation. In this research, the performance of copula-based models and ARCH-based models including VAR-GARCH, copula, and copula-GARCH models was then evaluated to simulate the annual maximum discharge values. The simulation results of all three models were evaluated using NSE and NRMSE statistics. According to the 95% confidence intervals, the accuracy of all three models was confirmed. The correlation results of the studied pair variables confirmed the possibility of using copula-based models. The results of simulations revealed that a higher accuracy of the copula-GARCH approach compared with two models copula and VAR-GARCH. Considering 76% efficiency (NSE = 0.76) of the copula-GARCH approach, the results indicated 20 and 2.7% improvements in the performance of the proposed approach compared to both VAR-GARCH and copula models. The results also illustrated that by combining nonlinear ARCH models with copula-based simulations, the reliability of simulation results increased. The results obtained in this study suggest that the proposed method is very effective for increasing the certainty of frequency analysis of two variables. Because the copula-GARCH approach simulates the average values, the first and third quarters, as well as the amplitude of changes of 5 and 95% of the data better than the other two models.Graphical abstractViolin plot of AMD series in copula scale

A regime-switching real-time copula GARCH model for optimal futures hedging

A regime-switching real-time copula GARCH (RSRTCG) model is suggested for optimal futures hedging. The specification of RSRTCG is to model the margins of asset returns with state-dependent real-time GARCH and the dependence structure of asset returns with regime switching copula functions. RSRTCG is faster in adjusting to the new level of volatility under different market regimes which is a regime-switching multivariate generalization of the state-independent univariate real-time GARCH. RSRTCG is applied to cross hedge the price risk of S&P 500 sector indices with crude oil futures. The empirical results show that RSRTCG possesses superior hedging performance compared to its nested non-real-time or state-independent copula GARCH models based on the criterion of percentage variance reduction, utility gain, model confidence set, model combination strategy, risk-adjusted return and reward-to-semivariance ratio.

Volatility research of nickel futures and spot prices based on copula-GARCH model

Nickel, an essential strategic emerging mineral in China, plays a vital role in promoting the development of the new energy vehicle industry and protecting the security of energy resources. However, the linkage between international and domestic nickel futures markets and the spot market is increasing. It is necessary to analyze and study the correlation characteristics and influence mechanisms to help investors avoid risks and judge the market situation which will improve the risk control ability and promote the steady development of the domestic market. Therefore, from the perspective of international and domestic markets and based on the yield sequence of the nickel futures prices and the spot prices, the study first discusses the characteristics of the volatility aggregation effect and asymmetries of the nickel futures and spot prices. Second, select an appropriate GARCH model to fit the marginal distribution sequence of the yields. Third, use the Copula function to connect the financial time series to find the correlation. The results indicate that the Copula-GARCH model can better fit the tail correlation between nickel futures market and spot market. Finally, we put forward policy recommendations for strengthening and improving the domestic nickel futures market, actively participating in the international competition mechanism, and preventing and controlling the risk of market price fluctuations.

Conditional Dynamic Dependence and Risk Spillover between Crude Oil Prices and Foreign Exchange Rates: New Evidence from a Dynamic Factor Copula Model

This paper proposes a dynamic factor model to accurately characterize the dynamic dependence and risk spillovers between the crude oil and exchange rate returns of oil-trading countries from 2000–2020, conditional on the common factors. To this end, we first identify the common factors related to returns of crude oil prices and exchange rates from 14 typical oil-trading countries. Then, we use the AR-GARCH model to filter the respective idiosyncratic factors and conduct a comparative study of conditional dynamic dependence between the crude oil and exchange rate returns of oil importers and exporters. Finally, we combine the dynamic factor copula model with the CoVaR method to measure the conditional risk spillover effect between crude oil and exchange rate markets. The empirical study indicates that the classical factor analysis can be used to precisely identify the common factors related to both financial markets, with the similar trend of macro-economic indicators. Furthermore, the factor copula model can capture the dynamic structure between crude oil and exchange rate markets more accurately than the traditional Copula–GARCH model. Specifically, the idiosyncratic factors related to each return series still have a significant impact on the dependence between the crude oil and exchange rate returns of oil importers, while the common factors have played an important role in the relationship of oil exporters’ exchange rates with crude oil prices. Finally, the crude oil market has enjoyed a relative risk premium to the exchange rate markets of oil-trading countries. However, there is almost no conditional risk spillover from the corresponding exchange rates to the crude oil prices. Finally, we discuss the implications for investors, policymakers and respective exchange rate regulators from oil-trading countries with further insights from the macro-economic perspective.

Dependence structure of CAT bonds and portfolio diversification: a copula-GARCH approach

This paper analyzes advantages of investing in catastrophe bonds (CATs) in terms of portfolio diversification. Indeed, the increase in environmental disasters and their economic and financial consequences are still poorly covered by insurance and reinsurance companies. As a result, there is a rapid growth in the use of catastrophe bonds on the financial markets, which can allow the transfer of risks to the capital market. We use copula-GARCH models to test the time-varying dependence of CATs, in a portfolio composed of six stock markets (CAC 40, DJIA, EUROSTOXX 50, FTSE 100, HANGSENG, and NIKKEI 225). Our results reveal that the CATs display the highest risk-adjusted performer. This security may be a good complement to a portfolio for investors seeking to optimize their risk-adjusted returns. In addition, the CATs are one of the best diversifiers. Finally, the CATs are the asset that increases the lowest the probability of extreme co-variations with its benchmark portfolio.

Hedging IMO2020 compliant fuel price exposure using futures contracts

The IMO 2020 sulphur cap regulation, requiring shipping companies to reduce air pollution of their vessels, poses significant challenges for these companies in terms of bunker risk management. This paper examines for the first time the cross-hedging performance of several petroleum futures contracts which may be used to manage the new low sulphur bunker spot price exposure in the three major bunker hub ports of the world supplying such fuels. Using copula-GARCH models, among others we show that the most effective hedge for the price risk of the low sulphur marine gasoil, through the use of the corresponding futures contracts, is achieved in the port of Singapore in comparison to that achieved in the ports of Rotterdam and Houston. Petroleum futures in the middle distillates family (ultra-low sulphur diesel, and low sulphur gasoil) are shown to be more effective than other petroleum products in reducing return variability. The copula-based strategy performs only marginally better out-of-sample than the rest of the methods employed. The findings provide significant implications and can guide shipping companies' bunker risk management regarding the hedging decisions on bunkering port, the hedging instrument, and the optimal hedging strategy.

Exploring dependence structures among European electricity markets: Static and dynamic copula-GARCH and dynamic state-space approaches

In this paper, we examine various characteristics of both base and peak electricity spot prices and their returns, and investigate dependence structures, extreme co-movements, risk spillovers, and integration relationships among the five major European electricity markets, including France, Germany, the Netherlands, Spain, and the UK. To do so, we propose a new perspective by applying a hybrid of ARMA-GARCH, static and dynamic copulas, and dynamic state-space models with the Kalman filter to address the issue. Based on the results of the ARMA-GJR-GARCH model, we first find that there are spillover effects in the returns of both base and peak spot prices in the five European electricity markets, and there are heteroskedastic, asymmetric, and leverage effects with negative and positive shocks, including spikes and drops during both base and peak load periods. Hence, a decrease in prices will boom the variance of the returns, and a decrease in returns can lead to a much greater increase in volatility. Second, there exist some extents of positive dependencies, tail dependencies, and extreme co-movements among the European electricity markets based on the copula models. In addition, we find that the degree of (tail) dependence and the potential state of market integration are stronger and higher during the peak period than the base period, implying that the European electricity markets could boom or crash together, especially during the peak load period. Further, the results of both the dynamic copulas and dynamic state-space models show that most pairs of the European electricity markets co-move symmetrically and have a time-varying dependence, but do not appear to grow over time. Finally, we provide an application of the copula-GARCH model in estimating and predicting risk spillovers across the five European electricity markets. We document that there are high-risk spillover effects in the European electricity markets because the values of the Conditional Value-at-Risk (CoVaR) are large. Also, we find that the more integrated the market, the more the systematic risk contribution of the market as indicated by ΔCoVaR. Our findings provide useful information regarding the dependence, integration, risk management, and asset pricing for the European electricity markets.

Copulas and Portfolios in the Electric Vehicle Sector

How can investors unlock the returns on the electric vehicle industry? Available investment choices range from individual stocks to exchange traded funds. We select six representative assets and characterize the time-varying joint distribution of their returns by copula-GARCH models. They facilitate portfolio optimization targeted at a chosen combination of risk and reward. With daily data from 2012 to 2020, we illustrate the models’ applicability by building a minimum expected shortfall portfolio and comparing its performance to that of an equally weighted benchmark. Our results should be of interest to investors and risk managers seeking or facing exposure to the electric vehicle sector.

Adoption of deep learning Markov model combined with copula function in portfolio risk measurement

Abstract In order to accurately describe the risk dependence structure and correlation between financial variables, a scientific financial risk assessment was carried out, and the basis for accurate financial decision-making was provided; the basic theory of copula function is established first, and the mixed copula model is constructed; then, the hybrid copula model is nested in a hidden Markov model (HMM); the risk dependences among banking, insurance, securities and trust industries are analysed, and the Copula-Garch model is constructed for empirical analysis of investment portfolio; finally, the deep learning Markov model is adopted to predict the financial index. The results show that the mixed copula model based on the HMM is more effective than the single copula model and the mixed copula model. The empirical structure shows that among the four major financial industries in China, banking and insurance industries have strong interdependence and a high probability of risk contagion. The investment failure rate under 95%, 97.5% and 99% confidence intervals calculated by the Copula-Garch model is 4.53%, 2.17% and 1.08%, respectively. Moreover, the errors of the deep learning Markov model in stock price prediction of Shanghai Pudong Development Bank (sh600000), Guizhou Moutai (sh600519) and China Ping An Insurance (sh601318) are 2.56%, 2.98% and 3.56%, respectively, which indicates that the four major financial industries in China have strong interdependence and risk contagion so that the macro or systemic risks may arise, and the deep learning Markov model can be adopted to predict the stock prices.

Adoption of deep learning Markov model combined with copula function in portfolio risk measurement

Abstract In order to accurately describe the risk dependence structure and correlation between financial variables, carry out scientific financial risk assessment, and provide the basis for accurate financial decision-making, first the basic theory of Copula function is established and the mixed Copula model is constructed. Then the hybrid Copula model is nested in a hidden Markov model (HMM), the risk dependences among banking, insurance, securities and trust industries are analysed, and the Copula–Garch model is constructed for empirical analysis of investment portfolio. Finally, the deep learning Markov model is adopted to predict the financial index. The results show that the mixed Copula model based on HMM is more effective than the single Copula and the mixed Copula models. The empirical structure shows that among the four major financial industries in China, the banking and insurance industries have strong interdependence and high probability of risk contagion. The investment failure rate under 95%, 97.5% and 99% confidence intervals calculated by Copula–Garch model are 4.53%, 2.17% and 1.08%, respectively. Moreover, the errors of deep learning Markov model in stock price prediction of Shanghai Pudong Development Bank (sh600000), Guizhou Moutai (sh600519) and China Ping An Insurance (sh601318) are 2.56%, 2.98% and 3.56% respectively, which indicates that the four major financial industries in China have strong interdependence and risk contagion, so that the macro or systemic risks may arise, and the deep-learning Markov model can be adopted to predict the stock prices.

Research on systemic risk contagion of Chinese financial institutions based on GARCH-VMD-Copula-CoVaR model

With the development of China's financial market, the risk contagion effect among financial institutions is increasing and becoming more complicated. Few literatures have explored the risk transmission paths of Chinese financial institutions at different frequencies. In order to make up for the gaps in this research field, variable mode decomposition (VMD) technology is introduced in this paper, combined with the Copula-GARCH model to construct the GARCH-VMD-Copula-CoVaR model, which describes the risk contagion paths of major financial institutions in the Chinese financial market at different frequencies (long-term, medium-term and short-term). The research results show that risk dependence and contagion between financial institutions have the characteristics of bidirectionality, asymmetry and time-varying in all frequency studies, and there are differences in different frequencies.

The asymmetric contagion effect between stock market and cryptocurrency market

This paper studies asymmetric contagion effects between stock and cryptocurrency markets. We implement the time-varying symmetrized Joe-Clayton copula GARCH model and Bai-Perron breakpoint test to explore dynamic correlations between the daily log-returns of the two markets in each time range. The asymmetric contagion effects between the two markets are studied using the non-linear Granger causality test. We also find that the lower tail dependences are more significant than the upper ones. Our findings can be used as a reference for supervisory authorities, and also provide insights on risk hedging for rational investors to avoid underestimating risk when building their portfolios.

Euro, dollar or Swiss franc: which currency had the greatest impact on the Hungarian, Polish and Czech economies during the global financial crisis?

The article presents an analysis of the impact of foreign currency dynamics on the fundamentals (basic indices of the economic performance) of the Czech Republic, Hungary and Poland during the financial crisis of 2007/2008 and its aftermath until 2017. The subject of the analysis are three currencies: the US dollar, the euro and the Swiss franc. The assessment of their impact on the fundamentals of the three above-mentioned economies is based on the joint volatilities of bond spreads and currencies. A series of copula-GARCH models was estimated. The research demonstrates that the impact of foreign currencies was the strongest in the case of Poland and Hungary, as these two countries were more dependent on loans in foreign currencies than the Czech Republic. Another finding shows that the impact decreased significantly in Hungary after its government introduced loan conversion.

Freight rate co-movement and risk spillovers in the product tanker shipping market: A copula analysis

Tanker shipping is a crucial sector carrying energy products across regions worldwide. This paper examines freight rate return dependencies across six major clean product tanker shipping routes by the copula-GARCH model. Using information from marginal and copula models, extreme risk spillover effects between different routes are further examined by the conditional Value-at-Risk (CoVaR) measure. Results reveal that the product tanker shipping market is regionalized and segmented by geographical locations. The dependency is high for different size ships operating in the same trade routes, while freight rates of ships having same sizes operating in adjacent regions have higher dependencies than operating in distant areas. Extreme co-movements exist in most return pairs with significant tail dependence. We further document significant extreme risk spillovers especially between adjacent or same trading routes and such spillover effects are found to be asymmetric in bearish and bullish markets. Our findings provide implications for shipping risk management.

A Personalized Mean-CVaR Portfolio Optimization Model for Individual Investment

Investment as an important issue in daily life is accompanied by the occurrence of various financial assets, such as stocks, bonds, and mutual funds. However, risk tolerances vary across individuals. Individual investors have to select corresponding personalized investment portfolios to satisfy their own needs. Moreover, it is difficult for ordinary people to select a personalized investment portfolio by themselves, and it is too expensive and inefficient to look for professional consultation. Therefore, the objective of this research is to propose a personalized portfolio recommendation model, which can build the personalized portfolio based on investors’ risk tolerances. In this research, investors’ risk tolerance is determined by the fuzzy comprehensive evaluation method based on investors’ demographic characteristics. The CVaR is used as the risk measurement of financial assets. The dynamics of the distribution of returns are described in the combined Copula-GARCH model, and the future scenarios of returns are generated by the Monte Carlo simulation based on the combined Copula-GARCH model to estimate CVaR. The mean-CVaR portfolio optimization model is used to find out the best personalized portfolio. Finally, experiments are conducted to validate the applicability and feasibility of the personalized investment portfolio optimization model. Results show that the proposed investment portfolio optimization model can recommend personalized investment portfolio according to investor’s risk tolerance.

Marginals Versus Copulas: Which Account For More Model Risk In Multivariate Risk Forecasting?

Copulas. We study the model risk of multivariate risk models in a comprehensive empirical study on Copula-GARCH models used for forecasting Value-at-Risk and Expected Shortfall. To determine whether model risk inherent in the forecasting of portfolio risk is caused by the candidate marginal or copula models, we analyze different groups of models in which we fix either the marginals, the copula, or neither. Model risk is economically significant, is especially high during periods of crisis, and is almost completely due to the choice of the copula. We then propose the use of the model confidence set procedure to narrow down the set of available models and reduce model risk for Copula-GARCH risk models. Our proposed approach leads to a significant improvement in the mean absolute deviation of one day ahead forecasts by our various candidate risk models.

Hedging agriculture commodities futures with histogram data: a Markov switching volatility and correlation model

In this study, the bivariate flexible Markov switching dynamic copula GARCH model is developed to histogram-value data for calculating optimal portfolio weight and optimal hedge. This model is an e...