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What copulas are, their estimation, and use is illustrated using a geographical diversification example. To accomplish this, dependencies between county-level yields are calculated for non-irrigated wheat, upland cotton, and sorghum using Pearson linear correlation and Kendall's tau. The use of Kendall's tau allows the implementation of copulas to estimate the dependency between county-level yields. The paper aims to discuss these issues.

Four parametric copulas, Gaussian, Frank, Clayton, and Gumbel, are used to estimate Kendall's tau. These four estimates of Kendall's tau are compared to Pearson's linear correlation, a more typical measure of dependence. Using this information, functions are estimated to determine the relationships between dependencies and changes in geographic and climate data.

The effect on county-level crop yields based on changes of geographical and climate variables differed among the different dependency measures among the three different crops. Implementing alternative dependency measures changed the statistical significance and the signs of the coefficients in the sorghum and cotton dependence functions. Copula-based elasticities are consistently less than the linear correlation elasticities for wheat and cotton. For sorghum, however, the copula-based elasticities are generally larger. The results indicate that one should not take the issue of measuring dependence as a trivial matter.

This research not only extends the current literature on geographical diversification by taking a more detailed examination of factors impacting yield dependence, but also extends the copula literature by comparing estimation results using linear correlation and copula-based rank correlation.

This paper aims to examine the evidence of risk spillovers between Shanghai and London non-ferrous futures markets using a dynamic Copula-CoVaR approach.

With daily data, the marginal distributions and optimal Copula functions are determined using the kernel estimation method and squared Euclidean distance test. The conditional value-at-risk and the conditional value-at-risk spillover rate are computed from the Copula estimated parameters based on the Copula-CoVaR model. Also, the dynamic correlation coefficient between the two futures markets is investigated.

The empirical results are as follows: overall, the risk spillover effect exerted by the London Metal Exchange on the Shanghai Futures Exchange is more significant than vice versa. Moreover, the degree of risk spillovers exerted by the London Metal Exchange on the Shanghai Futures Exchange for zinc and copper are more significant when they are depressed in the London Metal Exchange. Moreover, the dynamic of the correlation between the Shanghai and London futures markets is attributed to be largely due to changes in the global economy.

The Copula-CoVaR model used in this paper is suitable for measuring the risk spillovers between two different markets, while the risk spillovers across multiple markets or the consideration of multiple risk factors cannot be accurately captured using this framework. Multiple state variables to capture time variation in the conditional moments of return series will be a topic in future research.

The results provide theoretical support for risk management and monitoring of the non-ferrous futures markets.

The ability of the Copula function to accurately describe a nonlinear relationship and tail correlation is harnessed to measure the risk spillovers, explore the degree and direction of risk spillovers and identify the source of risk spillovers. The global economy is incorporated as a macro factor to explore its inner connection with the dynamic of risk spillovers in the non-ferrous metal futures market.

The purpose of this paper is to provide a new method to estimate the reliability of series system by using copula functions. This problem is of great interest in industrial and engineering applications.

The authors introduce copula functions and consider a Bayesian analysis for the proposed models with application to the simulated data.

The use of copula functions for modeling the bivariate distribution could be a good alternative to estimate the reliability of a two components series system. From the results of this study, the authors observe that they get accurate Bayesian inferences for the reliability function considering large samples sizes. The Bayesian parametric models proposed also allow the assessment of system reliability for multicomponent systems simultaneously.

Usually, the studies of systems reliability engineering assume independence among the component lifetimes. In the approach the authors consider a dependence structure. Using standard classical inference methods based on asymptotical normality of the maximum likelihood estimators for the parameters the authors could have great computational difficulties and possibly, not accurate inference results, which there is not found in the approach.

Purpose – In this chapter, copula theory is used to model dependence structure between hedge fund returns series.

Methodology/approach – Goodness-of-fit tests, based on the Kendall's functions, are applied as selection criteria of the “best” copula. After estimating the parametric copula that best fits the used data, we apply previous results to construct the cumulative distribution functions of the equally weighted portfolios.

Findings – The empirical validation shows that copula clearly allows better estimation of portfolio returns including hedge funds. The three studied portfolios reject the assumption of multivariate normality of returns. The chosen structure is often of Student type when only indices are considered. In the case of portfolios composed by only hedge funds, the dependence structure is of Franck type.

Originality/value of the chapter – Introducing goodness-of-fit bootstrap method to validate the choice of the best structure of dependence is relevant for hedge fund portfolios. Copulas would be introduced to provide better estimations of performance measures.

This paper aims to capture tail dependence between sentiment index and Shanghai composite index (SCI) by proposing a sentiment index based on text mining.

Online text mining and the Copula model were used in this study.

First, the paper finds herding effect in the expression of investors’ sentiment from online text data, and the usage occurrence frequency of most vocabulary is less correlative with SCI. Second, given these two features, the paper uses weighted divide-and-conquer algorithm to construct a sentiment index. Finally, because of multivariate non-Gaussian joint distribution between them, the paper uses the Copula model to detect their tail dependences, and finds that both upper and lower tail dependences could have a significant influence between positive sentiment and SCI, with a higher probability on the upper one. Additionally, only the upper tail dependence exhibits the significant influence between negative sentiment and SCI.

This paper proposes a framework of constructing investment sentiment index with the weighted conquer-and-divide algorithm, and characterizes tail dependence between sentiment index and SCI. The implication can measure the environment of investment market of China and provide an empirical ground for bandwagon effect and bargain shopper effect.

The purpose of this paper is to explore the dynamic interdependence structure and risk spillover effect between the Chinese stock market and the US stock market.

This paper mainly uses the multivariate R-vine copula-complex network analysis and the multivariate R-vine copula-CoVaR model and selects stock price indices and their subsector indices as samples.

The empirical results indicate that the Energy, Materials and Financials sectors have leading roles in the interdependent structure of the Chinese and US stock markets, while the Utilities and Real Estate sectors have the least important positions. The comprehensive influence of the Chinese stock market is similar to that of the US stock market but with smaller differences in the influence of different sectors of the US stock market on the overall interdependent structure system. Over time, the interdependent structure of both stock markets changed; the sector status gradually equalized; the contribution of the same sector in different countries to the interdependent structure converged; and the degree of interaction between the two stock markets was positively correlated with the degree of market volatility.

This paper employs the methods of nonlinear cointegration and the R-vine copula function to explore the interactive relationship and risk spillover effect between the Chinese stock market and the US stock market. This paper proposes the R-vine copula-complex network analysis method to creatively construct the interdependent network structure of the two stock markets. This paper combines the generalized CoVaR method with the R-vine copula function, introduces the stock market decline and rise risk and further discusses the risk spillover effect between the two stock markets.

The aim of this paper is to study the impact of equity returns volatility of reference entities on credit‐default swap rates using a new dataset from the Japanese market.

Using a copula approach, the paper models the different relationships that can exist in different ranges of behavior. It studies the bivariate distributions of credit‐default swap rates and equity return volatility estimated with GARCH (1,1) and focus on one parameter Archimedean copula.

First, the paper emphasizes the finding that pairs with higher rating present a weaker dependence coefficient and then, the impact of equity returns volatility on credit‐default swap rates is higher for the lowest rating class. Second, the dependence structure is positive and asymmetric indicating that protection sellers ask for higher credit‐default swap returns to compensate the higher credit risk incurred by low rating class.

The paper has several practical implications that are of value for financial hedgers and engineers, loan market participants, financial regulators, government regulators, central banks, and risk managers.

The paper also illustrates the potential benefits of equity returns volatility of reference entities as a proxy of default risk. These simplifications could be lifted in future research on this theme.

Knowledge of the dependence structure between financial assets is crucial to improve the performance in financial risk management. It is known that the copula completely summarizes the dependence structure among multiple variables. We propose a multivariate exponential series estimator (ESE) to estimate copula densities nonparametrically. The ESE has an appealing information-theoretic interpretation and attains the optimal rate of convergence for nonparametric density estimations in Stone (1982). More importantly, it overcomes the boundary bias of conventional nonparametric copula estimators. Our extensive Monte Carlo studies show the proposed estimator outperforms the kernel and the log-spline estimators in copula estimation. It also demonstrates that two-step density estimation through an ESE copula often outperforms direct estimation of joint densities. Finally, the ESE copula provides superior estimates of tail dependence compared to the empirical tail index coefficient. An empirical examination of the Asian financial markets using the proposed method is provided.

This research provides some evidence by the vine copula approach, suggesting the significant and symmetric causal relation between subsections of Baltic Exchange and hence concluding that investing in different indexes, which is currently a risk diversification system, is not a correct risk reduction strategy.

The daily observations of Baltic Capesize Index (BCI), Baltic Handysize Index (BHSI), Baltic Dirty Tanker Index (BDTI) and Baltic LNG Tanker Index (BLNG) over an eight-year period have been used. After collecting data, calculating the return and estimating the marginal distribution of return rates for each of the indexes applying asymmetric power generalized autoregressive conditional heteroskedasticity and autoregressive moving average (APGARCH-ARMA), and with the assumption of skew student's t-distribution, the dependence of Baltic indexes was modeled based on Vine-R structures.

A positive and symmetrical correlation was observed between the study groups. High and low tail dependence is observed between all four indexes. In other words, the sector business groups associated with each of these indexes react similarly to the extreme events of other groups. The BHSI has a pivotal role in examining the dependency structure of Baltic Exchange indexes. That is, in addition to the direct dependence of Baltic groups, the dependence of each group on the BHSI can transmit accidents and shocks to other groups.

Since the Baltic Exchange indexes are tradable, these findings have implications for portfolio design and hedging strategies for investors in shipping markets.

Vine copula structures proves the causal relationship between different Baltic Exchange indexes, which are derived from different types of markets.

The purpose of this paper is to study the correlation structure of the credit spreads.

The minimal spanning tree is used to find the risk center node and the basic correlation structure of the credit spreads. The dynamic copula and pair copula models are applied to capture the dynamic and non-linear correlation structure.

The authors take the enterprise bond with trading data from January 2013 to December 2013 as the research sample. The empirical study of minimum spanning tree shows that the credit risk of corporate bonds forms a network structure with a center node. Meanwhile, the correlation between credit spreads shows dynamic characteristics. Under the framework of dynamic copula, the lower tail dependence is less than the upper tail dependence, thus, in economic boom period, the dynamic correlation is more significant than in recession period. The authors also find that the centrality of credit risk network is not significant according to the pair copula and Granger causality test. The empirical study shows that the goodness-of-fit of D vine is superior to Canonical vine, and the Granger causality test additionally proves that the center node has influence on few other nodes in the risk network, thus the center node captured by the minimum spanning tree is a weak center node, and this characteristic of credit risk network indicates that the risk network of credit spreads is generated mostly by the external shocks rather than the internal risk contagion.

This paper provides new ideas for investors and researchers to analyze the credit risk correlation or contagion.