Are the interdependence characteristics of the US and Canadian energy equity sectors nonlinear and asymmetric?

Nonlinear, symmetric, and asymmetric dependence characteristics in energy equity sectors matter to portfolio investors and risk managers because of the risks and diversification opportunities they entail. Specifically, nonlinear dependence dynamics between assets are harder to predict, monitor, and manage, and can make investment positions go wrong unexpectedly. In this paper, we investigate whether the dependence dynamics of US and Canadian large-capitalized energy equity portfolios are nonlinear, symmetric, or asymmetric. We draw our results by implementing a robust copula approach based on time-varying parameter copulas and vine copula methods. Both time varying parameter and vine-copula methods indicate that the Canadian energy sector portfolio is driven by nonlinear negative tail asymmetric dependence during the global financial crisis and when the full sample period is employed. On the other hand, it displays nonlinear symmetric dependence during the oil price crisis, implying the need for close monitoring and rebalancing and a more continuous assessment of long investment positions. The US energy sector portfolio is driven by positive tail asymmetric dependence, and by symmetric dependence dynamics during crisis and non-crisis periods.     

The t Copula and Related Copulas

The t copula and its properties are described with a focus on issues related to the dependence of extreme values. The Gaussian mixture representation of a multivariate t distribution is used as a starting point to construct two new copulas, the skewed t copula and the grouped t copula, which allow more heterogeneity in the modelling of dependent observations. Extreme value considerations are used to derive two further new copulas: the t extreme value copula is the limiting copula of componentwise maxima of t distributed random vectors; the t lower tail copula is the limiting copula of bivariate observations from a t distribution that are conditioned to lie below some joint threshold that is progressively lowered. Both these copulas may be approximated for practical purposes by simpler, better-known copulas, these being the Gumbel and Clayton copulas respectively.     

Financial dependence analysis: applications of vine copulas

This paper features the application of a novel and recently developed method of statistical and mathematical analysis to the assessment of financial risk, namely regular vine copulas. Dependence modelling using copulas is a popular tool in financial applications but is usually applied to pairs of securities. Vine copulas offer greater flexibility and permit the modelling of complex dependence patterns using the rich variety of bivariate copulas that can be arranged and analysed in a tree structure to facilitate the analysis of multiple dependencies. We apply regular vine copula analysis to a sample of stocks comprising the Dow Jones index to assess their interdependencies and to assess how their correlations change in different economic circumstances using three different sample periods around Global Financial Crisis (GFC).: pre‐GFC (January 2005 to July 2007), GFC (July 2007 to September 2009) and post‐GFC periods (September 2009 to December 2011). The empirical results suggest that the dependencies change in a complex manner, and there is evidence of greater reliance on the Student‐t copula in the copula choice within the tree structures for the GFC period, which is consistent with the existence of larger tails in the distributions of returns for this period. One of the attractions of this approach to risk modelling is the flexibility in the choice of distributions used to model co‐dependencies. The practical application of regular vine metrics is demonstrated via an example of the calculation of the Value at Risk of a portfolio of stocks.     

A new extension of bivariate FGM copulas

We propose a new family of copulas generalizing the Farlie–Gumbel–Morgenstern family and generated by two univariate functions. The main feature of this family is to permit the modeling of high positive dependence. In particular, it is established that the range of the Spearman’s Rho is [ − 3/4,1] and that the upper tail dependence coefficient can reach any value in [0,1]. Necessary and sufficient conditions are given on the generating functions in order to obtain various dependence properties. Some examples of parametric subfamilies are provided.     

Analysing contagion and bailout effects with copulae

In this paper, a new methodical framework that combines elements of event studies and copula methodology is proposed in the context of the analysis of bank contagion. Furthermore, to the best knowledge of the author, this paper is the first one to analyse changes in the dependence structure of banks around bailout announcements. The results of the empirical study show that significant contagion effects could be detected both in the German banking sector after the onset of the subprime crisis as well as in the Japanese banking sector in the mid-nineties. I find that announcements of crisis at struggling banks induce a significant increase of lower tail dependence in the banking sector. The analysed bailouts and rescue measures by the central bank proved to be effective in reducing this increased lower tail dependence while increasing tail independence of bank stock returns at the same time. In both data samples, I find that the bailout announcements did not simply restore the pre-crisis dependence structure, but rather only decreased the likelihood of a joint crash of bank stocks without increasing the chances of a joint boom.     

Predicting the portfolio risk of high-dimensional international stock indices with dynamic spatial dependence

The spatial dependence of assets, which relates to similarities in economic, political, or cultural systems and other aspects, has been confirmed through empirical research; however, spatial dependence has rarely been applied to financial risk measurement. To fill this gap in the literature, a dynamic spatial GARCH-copula (sGC) model is proposed in this paper to evaluate the portfolio risk of international stock indices. In this model, a spatial GARCH is used as the marginal distribution and vine copula is adopted as the joint distribution of indices. Then, the proposed model is applied empirically to assess portfolio risk. Results show that, first, the proposed risk prediction model with spatial dependence outperforms a model neglecting spatial effects per the Kupiec test, Z test and Christoffersen test. Risk prediction during periods of economic stability is also more accurate than during times of crisis. Second, risk measures for models with spatial dependence are higher than those without such dependence but lower than for vine copula models. Third, models including either spatial dependence or vine copulas alone exhibit relatively poor performance. Fourth, the model involving extreme value theory (EVT) generates the greatest value at risk to pass the Kupiec test, Z test and Christoffersen test; however, this model is not suitable for characterizing international indices with EVT based on negative values of the shape parameters of estimates. Findings offer important implications for personal investors, institutional investors, and national regulatory authorities.     

The conditional dependence structure of insurance sector credit default swap indices

This study assesses the dependence structure of insurance sector credit default swap indices, using a copula-GARCH approach. We use daily data of the US, EU, and UK insurance sectors, covering the period from January 2004 to June 2013. We find substantial increases in dependence during the financial crisis periods. Prior to the crises, various copulas are found to best fit each pair; specifically, asymmetric tail dependence is found for the UK–US pair, suggesting the possibility of large simultaneous losses. However, during the crisis periods, the Frank copula fits best, with no significant tail dependence detected, implying low systemic risks.     

An investigation on mixed housing-cycle structures and asymmetric tail dependences

This paper designs a Markov-switching mixture Copula-based model with a mixed Markov-transition mechanism to investigate the mixed housing-cycle structures and asymmetric tail dependences for the Pacific and Mountain divisions of American regional housing markets. The empirical results demonstrate four interesting findings. First, the Markov-switching process can capture the housing cycle of each housing market. Second, the evidence of the mixed Markov-switching specification indicates that the joint housing-cycle behaviors are related not only to the total dependence mechanism, but also to the independent mechanism. Specifically, each housing market has its own characteristics, and these characteristics play relatively more important roles in determining the joint housing-cycle pattern than do common factors related to the total dependence framework. Third, the two housing markets have asymmetric tail dependences. Tail dependence exists when two markets experience the same housing-cycle modes, but does not occur when two markets experience distinct housing-cycle modes. In addition, the intensity of tail dependence is stronger when two markets remain in recession mode, as opposed to when they remain in recovery mode. This finding suggests that downward price rigidity does not exist in regional housing markets. Fourth, the spillover effects between housing returns are asymmetric.     

An analysis of dependence between Central and Eastern European stock markets

We examine the dependence structure between four Central and Eastern European (CEE) stock markets (Czech Republic, Hungary, Poland and Romania) using static and dynamic copula functions with different forms of tail dependence. We find evidence of positive dependence between all CEE stock markets, although this dependence is stronger between the Hungarian, Czech and Polish markets than between these markets and the Romanian market. We also find evidence of symmetric tail dependence, although not for the Hungarian and Czech markets. The dependence is time-varying and intensified after the onset of the recent global financial crisis. These results confirm that CEE stock markets are gradually coupling, a fact that has risk management implications for policymakers and investors.     

Modelling soccer matches using bivariate discrete distributions with general dependence structure

In this paper copulas are used to generate bivariate discrete distributions. These distributions are fitted to soccer data from the English Premier League. An interesting aspect of these data is that the primary variable of interest, the discrete pair shots-for and shots-against, exhibits negative dependence; thus, in particular, we apply bivariate Poisson-related distributions that allow such dependence. The paper focuses on Archimedian copulas, for which the dependence structure is fully determined by a one-dimensional projection that is invariant under marginal transformations. Diagnostic plots for copula fit based on this projection are adapted to deal with discrete variables. Covariates relating to within-match contributions such as numbers of passes and tackles are introduced to explain variability in shot outcomes. The results of this analysis would appear to support the notion that playing the 'beautiful game' is an effective strategy—more passes and crosses contribute to more effective play and more shots on the goal.     

Inversion copulas from nonlinear state space models with an application to inflation forecasting

We propose the construction of copulas through the inversion of nonlinear state space models. These copulas allow for new time series models that have the same serial dependence structure as a state space model, but with an arbitrary marginal distribution, and flexible density forecasts. We examine the time series properties of the copulas, outline serial dependence measures, and estimate the models using likelihood-based methods. Copulas constructed from three example state space models are considered: a stochastic volatility model with an unobserved component, a Markov switching autoregression, and a Gaussian linear unobserved component model. We show that all three inversion copulas with flexible margins improve the fit and density forecasts of quarterly U.S. broad inflation and electricity inflation.     

Upside/Downside spillovers between oil and Chinese stock sectors: From the global financial crisis to global pandemic

This paper examines the effects of the COVID-19 outbreak, recent oil price fall, and both global and European financial crises on dependence structure and asymmetric risk spillovers between crude oil and Chinese stock sectors. Using time-varying symmetric and asymmetric copula functions and the conditional Value at Risk measure, we provide evidence of positive tail dependence in most sectors using copula and conditional Value-at-Risk techniques. We can see the average dependence between oil and industries during the oil crisis. Moreover, we find strong evidence of bidirectional risk spillovers for all oil-sector pairs. The intensity of risk spillovers from oil to all stock sectors varies across sectors. The risk spillovers from sectors to oil are substantially larger than those from oil to sectors during COVID-19. Furthermore, the return spillover is time varying and sensitive to external shocks. The spillover strengths are higher during COVID-19 than financial and oil crises. Finally, oil do not exhibit neither hedge nor safe-haven characteristics irrespective of crisis periods.     

A copula-based time series model for global horizontal irradiation

The increasing importance of solar power for electricity generation leads to increasing demand for probabilistic forecasting of local and aggregated photovoltaic (PV) yields. Based on publicly available irradiation data, this paper uses an indirect modeling approach for hourly medium to long-term local PV yields. We suggest a time series model for global horizontal irradiation that allows for multivariate probabilistic forecasts for arbitrary time horizons. It features several important stylized facts. Sharp time-dependent lower and upper bounds of global horizontal irradiations are estimated. The parameters of the beta distributed marginals of the transformed data are allowed to be time-dependent. A copula-based time series model is introduced for the hourly and daily dependence structure based on simple vine copulas with so-called tail dependence. Evaluation methods based on scoring rules are used to compare the model’s power for multivariate probabilistic forecasting with other models used in the literature showing that our model outperforms other models in many respects.     

Economic policy uncertainty and industry risk on China’s stock market

We propose a dynamic mixture Copula with time-varying weight, which is endowed with generalized autoregressive score dynamics. Based on this model, we portray the lower-tail dependence between the return of WIND first-level industry and CSI-300 index as a proxy variable for the industry risk in China’s stock market, and use the VAR-GARCH-in-mean model based on BEKK-GARCH to deconstruct the different impact of the economic policy uncertainty (EPU) on industry risk of the first and second moments in terms of four policy categories, namely fiscal policy, monetary policy, trade policy, and foreign exchange rate and capital account policy. The results are followed. Firstly, the risk of Consumer Discretionary is averagely the highest, while the risk of Utilities remains the lowest. Secondly, category-specific EPU has no significant mean spillover to the risk of overall industries, while the variance spillover is significant for all the cases. Thirdly, except for Real Estate, the GARCH-in-mean effect is not significant of EPU on industry risks. Further more, all those three kinds of impact show industrial heterogeneities. To avoid systemic risks, we advise that the issue of economic policy should be forward-looking, consistent, and targeted, especially for sensitive industries.     

Do cryptocurrencies provide better hedging? Evidence from major equity markets during COVID-19 pandemic

Using the five-minute interval price data of two cryptocurrencies and eight stock market indices, we examine the risk spillover and hedging effectiveness between these two assets. Our approach provides a comparative assessment encompassing the pre-COVID-19 and COVID-19 sample periods. We employ copula models to assess the dependence and risk spillover from Bitcoin and Ethereum to stock market returns during both the pre-COVID-19 and COVID-19 periods. Notably, the COVID-19 pandemic has increased the risk spillover from Bitcoin and Ethereum to stock market returns. The findings vis-à-vis portfolio weights and hedge effectiveness highlight hedging gains; however, optimal investments in Bitcoin and Ethereum have reduced during the COVID-19 pandemic, while the cost of hedging has increased during this period. The findings also confirm that cryptocurrencies cannot provide incremental gains by hedging stock market risk during the COVID-19 pandemic.     

Contagion effect of systemic risk among industry sectors in China’s stock market

This paper constructs a tail event driven network to investigate the interdependence of tail risks among industries in the Chinese stock market from 2014 to 2019, and identifies systemically important industries that have made significant contributions to risk contagion by systemic risk decomposition technique. The empirical results suggest strong linkages among industry sectors. The risk profiles of certain industries under close supply–demand relationships are positively correlated, whereas the financial industry, particularly banking, proves to be the principal risk diversifier in the network, with the household appliance, food and drink industries performing likewise an important role in risk diversification. Based on the TENQR model, further study on additional information provided by the industrial chain structure demonstrates that the upstream industry dominates the spread of risks under extreme market conditions. Our findings are of constructive significance to the anticipative introduction of corresponding policies by regulatory authorities, and are also instructive to the investors’ allocation of assets.     

The impact of the shutdown policy on the asymmetric interdependence structure and risk transmission of cryptocurrency and China’s financial market

By taking Bitcoin, Litecoin, and China’s gold and RMB/US dollar exchange rate market as research objects, this paper apply the MF-ADCCA and time-delayed DCCA methods to study the impact of China’s mainland shutdown of cryptocurrencies trading on the non-linear interdependent structure and risk transmission of cryptocurrencies and its financial market. Empirical results show that the cross-correlation between cryptocurrencies and China’s financial market has a long memory and asymmetric multifractal characteristics. After the shutdown, the long memory between cryptocurrencies and Chinese gold has weakened, and the long memory between cryptocurrencies and the RMB/US dollar exchange rate market was strengthened. China’s shutdown policy has a certain risk prevention effect. Specifically, after the implementation of the policy, the risk transmission of cryptocurrencies to China’s financial market has weakened, but the influence of China’s financial market has gradually strengthened.     

Diversification for general copula dependence

We generalize the extreme value analysis for Archimedean copulas (see Alink , Löwe and Wüthrich , 2003) to the non-Archimedean case: Assume we have d ≥2 exchangeable and continuously distributed risks X ₁,…, X _d . Under appropriate assumptions there is a constant q _d such that, for all large u , we have . The constant q _d describes the asymptotic dependence structure. Typically, q _d will depend on more aspects of this dependence structure than the well-known tail dependence coefficient.     

Risk spillover from crude oil prices to GCC stock market returns: New evidence during the COVID-19 outbreak

In this study, we examine oil price extreme tail risk spillover to individual Gulf Cooperation Council (GCC) stock markets and quantify this spillover’s shift before and during the COVID-19 pandemic. A dynamic conditional correlation generalized autoregressive heteroscedastic (DCC- GARCH) model is employed to estimate three important measures of tail dependence risk: conditional value at risk (CoVaR), delta CoVaR (ΔCoVaR), and marginal expected shortfall (MES). Using daily data from January 2017 until May 2020, results point to significant systemic oil risk spillover in all GCC stock markets. In particular, the effect of oil price systemic risk on GCC stock market returns was significantly larger during COVID-19 than before the pandemic. Upon splitting COVID-19 into two phases based on severity, we identify Saudi Arabia as the only GCC market to have experienced significantly higher exposure to oil risk in Phase 1. Although all GCC stock markets received greater oil systemic risk spillover in Phase 2 of COVID-19, Saudi Arabia and the United Arab Emirates appeared more vulnerable to oil extreme risk than other countries. Our empirical findings reveal that investors should carefully consider the extreme oil risk effects on GCC stock markets when designing optimal portfolio strategies, minimizing portfolio risk, and adopting dynamic diversification process. Policymakers and regulators should also enact awareness, oversight, and action plans to minimize adverse oil risk effects.     

Nonparametric inference on multivariate versions of Blomqvist’s beta and related measures of tail dependence

We consider nonparametric estimation of multivariate versions of Blomqvist’s beta, also known as the medial correlation coefficient. For a two-dimensional population, the sample version of Blomqvist’s beta describes the proportion of data which fall into the first or third quadrant of a two-way contingency table with cutting points being the sample medians. Asymptotic normality and strong consistency of the estimators are established by means of the empirical copula process, imposing weak conditions on the copula. Though the asymptotic variance takes a complicated form, we are able to derive explicit formulas for large families of copulas. For the copulas of elliptically contoured distributions we obtain a variance stabilizing transformation which is similar to Fisher’s z-transformation. This allows for an explicit construction of asymptotic confidence bands used for hypothesis testing and eases the analysis of asymptotic efficiency. The computational complexity of estimating Blomqvist’s beta corresponds to the sample size n, which is lower than the complexity of most competing dependence measures.