scholarly journals Lower Tail Dependence for Archimedean Copulas: Characterizations and Pitfalls

2006 ◽  
Author(s):  
Arthur Charpentier ◽  
Johan Segers
Keyword(s):  
Tail Dependence ◽  
Archimedean Copulas ◽  
Lower Tail

scholarly journals Extremal behavior of Archimedean copulas

2011 ◽  
Vol 43 (1) ◽  
pp. 195-216 ◽  
Author(s):  
Martin Larsson ◽  
Johanna Nešlehová
Keyword(s):  
Domain Of Attraction ◽  
Tail Dependence ◽  
Dependence Structure ◽  
Tail Behavior ◽  
Archimedean Copulas ◽  
Radial Part ◽  
Stochastic Representation ◽  
Lower Tail ◽  
Extremal Behavior ◽  
Practical Implications

We show how the extremal behavior of d-variate Archimedean copulas can be deduced from their stochastic representation as the survival dependence structure of an ℓ1-symmetric distribution (see McNeil and Nešlehová (2009)). We show that the extremal behavior of the radial part of the representation is determined by its Williamson d-transform. This leads in turn to simple proofs and extensions of recent results characterizing the domain of attraction of Archimedean copulas, their upper and lower tail-dependence indices, as well as their associated threshold copulas. We outline some of the practical implications of their results for the construction of Archimedean models with specific tail behavior and give counterexamples of Archimedean copulas whose coefficient of lower tail dependence does not exist.

scholarly journals Extremal behavior of Archimedean copulas

2011 ◽  
Vol 43 (01) ◽  
pp. 195-216 ◽  
Author(s):  
Martin Larsson ◽  
Johanna Nešlehová
Keyword(s):  
Domain Of Attraction ◽  
Tail Dependence ◽  
Dependence Structure ◽  
Tail Behavior ◽  
Archimedean Copulas ◽  
Radial Part ◽  
Stochastic Representation ◽  
Lower Tail ◽  
Extremal Behavior ◽  
Practical Implications

We show how the extremal behavior of d-variate Archimedean copulas can be deduced from their stochastic representation as the survival dependence structure of an ℓ1-symmetric distribution (see McNeil and Nešlehová (2009)). We show that the extremal behavior of the radial part of the representation is determined by its Williamson d-transform. This leads in turn to simple proofs and extensions of recent results characterizing the domain of attraction of Archimedean copulas, their upper and lower tail-dependence indices, as well as their associated threshold copulas. We outline some of the practical implications of their results for the construction of Archimedean models with specific tail behavior and give counterexamples of Archimedean copulas whose coefficient of lower tail dependence does not exist.

scholarly journals Spatial Tail Dependence and Survival Stability in a Class of Archimedean Copulas

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Diakarya Barro ◽  
Moumouni Diallo ◽  
Remi Guillaume Bagré
Keyword(s):  
Dimensional Analysis ◽  
Tail Dependence ◽  
High Dimensional ◽  
Archimedean Copulas ◽  
Lower Tail

This paper investigates properties of extensions of tail dependence of Archimax copulas to high dimensional analysis in a spatialized framework. Specifically, we propose a characterization of bivariate margins of spatial Archimax processes while spatial multivariate upper and lower tail dependence coefficients are modeled, respectively, for Archimedean copulas and Archimax ones. A property of stability is given using convex transformations of survival copulas in a spatialized Archimedean family.

scholarly journals Assessing Market Risk in BRICS and Oil Markets: An Application of Markov Switching and Vine Copula

2021 ◽  
Vol 9 (2) ◽  
pp. 30
Author(s):  
John Weirstrass Muteba Mwamba ◽  
Sutene Mwambetania Mwambi
Keyword(s):  
South Africa ◽  
Crude Oil ◽  
South African ◽  
Asset Allocation ◽  
Markov Switching ◽  
Tail Dependence ◽  
Lower Tail ◽  
Oil Market ◽  
Oil Markets ◽  
Vine Copula

This paper investigates the dynamic tail dependence risk between BRICS economies and the world energy market, in the context of the COVID-19 financial crisis of 2020, in order to determine optimal investment decisions based on risk metrics. For this purpose, we employ a combination of novel statistical techniques, including Vector Autoregressive (VAR), Markov-switching GJR-GARCH, and vine copula methods. Using a data set consisting of daily stock and world crude oil prices, we find evidence of a structure break in the volatility process, consisting of high and low persistence volatility processes, with a high persistence in the probabilities of transition between lower and higher volatility regimes, as well as the presence of leverage effects. Furthermore, our results based on the C-vine copula confirm the existence of two types of tail dependence: symmetric tail dependence between South Africa and China, South Africa and Russia, and South Africa and India, and asymmetric lower tail dependence between South Africa and Brazil, and South Africa and crude oil. For the purpose of diversification in these markets, we formulate an asset allocation problem using raw returns, MS GARCH returns, and C-vine and R-vine copula-based returns, and optimize it using a Particle Swarm optimization algorithm with a rebalancing strategy. The results demonstrate an inverse relationship between the risk contribution and asset allocation of South Africa and the crude oil market, supporting the existence of a lower tail dependence between them. This suggests that, when South African stocks are in distress, investors tend to shift their holdings in the oil market. Similar results are found between Russia and crude oil, as well as Brazil and crude oil. In the symmetric tail, South African asset allocation is found to have a well-diversified relationship with that of China, Russia, and India, suggesting that these three markets might be good investment destinations when things are not good in South Africa, and vice versa.

Multivariate extremes, aggregation and dependence in elliptical distributions

2002 ◽  
Vol 34 (03) ◽  
pp. 587-608 ◽  
Author(s):  
Henrik Hult ◽  
Filip Lindskog
Keyword(s):  
Random Vector ◽  
Positive Constant ◽  
Tail Dependence ◽  
Constant Factor ◽  
Dispersion Matrix ◽  
Elliptical Distributions ◽  
Spectral Measures ◽  
Lower Tail ◽  
Explicit Formulae ◽  
Dependence Properties

In this paper, we clarify dependence properties of elliptical distributions by deriving general but explicit formulae for the coefficients of upper and lower tail dependence and spectral measures with respect to different norms. We show that an elliptically distributed random vector is regularly varying if and only if the bivariate marginal distributions have tail dependence. Furthermore, the tail dependence coefficients are fully determined by the tail index of the random vector (or equivalently of its components) and the linear correlation coefficient. Whereas Kendall's tau is invariant in the class of elliptical distributions with continuous marginals and a fixed dispersion matrix, we show that this is not true for Spearman's rho. We also show that sums of elliptically distributed random vectors with the same dispersion matrix (up to a positive constant factor) remain elliptical if they are dependent only through their radial parts.

scholarly journals Forecasting portfolio-Value-at-Risk with nonparametric lower tail dependence estimates

2015 ◽  
Vol 54 ◽  
pp. 129-140 ◽  
Author(s):  
Karl Friedrich Siburg ◽  
Pavel Stoimenov ◽  
Gregor N.F. Weiß
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Tail Dependence ◽  
Lower Tail

scholarly journals Behaviour of multivariate tail dependence coefficients

2019 ◽  
Vol 22 (2) ◽  
pp. 299-310
Author(s):  
Gaida Pettere ◽  
Irina Voronova ◽  
Ilze Zariņa
Keyword(s):  
Risk Assessment ◽  
Simulation Experiment ◽  
Tail Dependence ◽  
Solvency Ii ◽  
Lower Tail ◽  
Alternative Method ◽  
T Copula ◽  
Dependence Property ◽  
Multivariate T ◽  
Tail Dependence Coefficient

In applications tail dependence is an important property of a copula. Bivariate tail dependence is investigated in many papers, but multivariate tail dependence has not been studied widely. We define multivariate upper and lower tail dependence coefficients as limits of the probability that values of one marginal will be large if at least one of other marginals will be as large also. Further we derive some relations between introduced tail dependence and bivariate tail dependence coefficients. Applications have shown that the multivariate t-copula has been successfully used in practice because of its tail dependence property. Therefore, t-copula can be used as an alternative method for risk assessment under Solvency II for insurance models. We have paid attention to the properties of the introduced multivariate tail dependence coefficient for t-copula and examine it in the simulation experiment.

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