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.

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 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 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

Assessment of Societal Risks Associated With Large Gas Transmission Pipeline Systems

2020 ◽  
Author(s):  
Dongliang Lu ◽  
Alex Tomic ◽  
Shahani Kariyawasam
Keyword(s):  
Risk Assessment ◽  
Natural Gas ◽  
Individual Risk ◽  
Risk Levels ◽  
Risk Criteria ◽  
Alternative Method ◽  
Societal Risk ◽  
Pipeline Systems ◽  
The Uk ◽  
Level Of Risk

Abstract Risk assessment is the process of risk analysis and evaluation. It is a required component of pipeline integrity management programs (IMP) and is generally the first step in most IMPs. For the risk assessment of natural gas pipelines, the primary concern is the safety of population near the pipeline right of way (ROW). TC Energy’s SWRA uses a quantitative risk assessment model that considers the effect of the thermal radiation due to ignited pipeline rupture and evaluate the consequence on the surrounding population. The overall risk is then evaluated using two specific risk criteria: societal risk and individual risk, with the societal risk measuring the overall level of risk to a community or a group of people and the individual risk measuring the level of risk to specific individuals who are present within the pipeline hazard zone. Natural gas pipeline systems often extend hundreds or even thousands of miles. As such, societal risk criteria for pipelines are typically defined based on a given length of pipeline segment, usually in 1 km or 1 mile (1.6 km). To assess the societal risk of actual pipelines, different approaches are taken on how the risk along the length of a pipeline should be aggregated and compared to the criteria. For example, the PD8010-3 standard in the UK recommends the societal risk of a pipeline through a community to be aggregated and then normalized to the unit length to be compared with criteria; whereas the Dutch regulation requires societal risk at the worst location to be used. In the current SWRA, the societal risk along the length of a pipeline going through development areas or communities is aggregated following the recommendation of the UK PD8010-3, where the risk is aggregated and normalized to the pipeline length. Due to the vast scale of the pipeline system, it is impractical to manually review all development along the pipelines for conducting societal risk assessment on a system wide basis. As such, extent of communities and development areas is determined by a computer program using a simple set of rules. It was found to have led to unsatisfying granularity in the societal risk assessment in certain situations, with some interaction lengths being too long and thus failing to identify the more critical section within the interaction length, and certain development lengths being too short and thus not very meaningful from a societal risk perspective. To overcome issues with the current societal risk assessment method in SWRA, an alternative method largely following the direction of the Dutch approach is introduced in this paper. In this alternative approach, the societal risk is evaluated continuously along a pipeline with a predefined a sliding length, and thus variations in the societal risk levels along the entire length of a pipeline, including the locations with the highest societal risk levels, can be identified. Implantation details and computational efficiency were discussed. The results from the alternative method were compared to that from the current method. The sensitivity of the sliding length method to the predefined sliding length was also investigated. The study showed that this alternative method improves the accuracy and granularity of the societal risk assessment in the SWRA, and, although it is relatively computational commanding, with an efficient implementation, is still practical even for very large gas transmission systems.

Dependence analysis on the seismic demands of typical components of a concrete continuous girder bridge with the copula technique

2018 ◽  
Vol 21 (12) ◽  
pp. 1826-1839 ◽  
Author(s):  
Shuai Song ◽  
Jing Liu ◽  
Yongjiu Qian ◽  
Fang Zhang ◽  
Gang Wu
Keyword(s):  
Ground Motion ◽  
Transverse Direction ◽  
Tail Dependence ◽  
Longitudinal Direction ◽  
Nonlinear Dependence ◽  
Lower Tail ◽  
Distance Method ◽  
Seismic Demands ◽  
Seismic Reliability ◽  
Bridge System

The seismic reliability of a bridge system is significantly affected by the dependence among typical bridge components. This study demonstrates the process of using a copula technique to describe the nonlinear dependence among component seismic demands isolated from their marginal probability distributions. A suite of 100 bridge-ground motion samples were developed with the Latin hypercube sampling approach and bin approach. Based on the incremental dynamic analysis, the tail dependence among component seismic demands at different intensity levels was analyzed with the best-fitting copula function selected by the minimum distance method. In the longitudinal direction, the dependence increased first and then decreased with the ground motion intensity, while the dependence slightly decreased in the transverse direction. At low-intensity levels, the upper tail dependence among components was strong in both directions. At high-intensity levels, the upper and lower tail dependences were weak in the longitudinal direction, while the upper and lower tail dependences were strong in the transverse direction. Compared to the linear correlation coefficient, the copula technique provides an efficient way to describe the tail dependence among component seismic demands and can be used extensively in the seismic reliability analysis of the bridge system.

Sign in / Sign up

Export Citation Format

Share Document