Regular Variation, Conditions of Domain of Attraction and the Existence of the Tail Dependence Function in the General Dependence Case: A Copula Approach

2020 ◽  
Vol 15 (1) ◽  
Author(s):  
Yuri Salazar Flores ◽  
Adán Díaz Hernández
Keyword(s):  
Regular Variation ◽  
Domain Of Attraction ◽  
Tail Dependence ◽  
Dependence Function ◽  
Copula Approach

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 On Conditional Value at Risk (CoVaR) for tail-dependent copulas

2017 ◽  
Vol 5 (1) ◽  
pp. 1-19 ◽  
Author(s):  
Piotr Jaworski
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Tail Dependence ◽  
Extreme Value ◽  
Conditional Value At Risk ◽  
Dependence Function ◽  
Conditioning Event

Abstract The paper deals with Conditional Value at Risk (CoVaR) for copulas with nontrivial tail dependence. We show that both in the standard and the modified settings, the tail dependence function determines the limiting properties of CoVaR as the conditioning event becomes more extreme. The results are illustrated with examples using the extreme value, conic and truncation invariant families of bivariate tail-dependent copulas.

scholarly journals Pareto Lévy Measures and Multivariate Regular Variation

2012 ◽  
Vol 44 (1) ◽  
pp. 117-138 ◽  
Author(s):  
Irmingard Eder ◽  
Claudia Klüppelberg
Keyword(s):  
Regular Variation ◽  
Lévy Process ◽  
Tail Dependence ◽  
Levy Process ◽  
Dependence Structure ◽  
Lévy Measure ◽  
Multivariate Distributions ◽  
One Dimensional ◽  
The One ◽  
Lévy Measures

We consider regular variation of a Lévy process X := (Xt)t≥0 in with Lévy measure Π, emphasizing the dependence between jumps of its components. By transforming the one-dimensional marginal Lévy measures to those of a standard 1-stable Lévy process, we decouple the marginal Lévy measures from the dependence structure. The dependence between the jumps is modeled by a so-called Pareto Lévy measure, which is a natural standardization in the context of regular variation. We characterize multivariate regularly variation of X by its one-dimensional marginal Lévy measures and the Pareto Lévy measure. Moreover, we define upper and lower tail dependence coefficients for the Lévy measure, which also apply to the multivariate distributions of the process. Finally, we present graphical tools to visualize the dependence structure in terms of the spectral density and the tail integral for homogeneous and nonhomogeneous Pareto Lévy measures.

scholarly journals Examining the Interdependence between the Exchange Rates of China and ASEAN Countries: A Canonical Vine Copula Approach

2019 ◽  
Vol 11 (19) ◽  
pp. 5487 ◽  
Author(s):  
Liu ◽  
Wang ◽  
Sriboonchitta
Keyword(s):  
Exchange Rates ◽  
Tail Dependence ◽  
Dependence Structure ◽  
Positive Dependence ◽  
Asymmetric Dependence ◽  
Before And After ◽  
Copula Approach ◽  
Asean Countries ◽  
Vine Copula ◽  
Vine Copulas

Based on the canonical vine (C-vine) copula approach, this paper examines the interdependence between the exchange rates of the Chinese Yuan (CNY) and the currencies of major Association of Southeast Asian Nations (ASEAN) countries. The differences in the dependence structure and degree between currencies before and after the Belt and Road (B&R) Initiative were compared in order to investigate the changing role of the Renminbi (RMB) in the ASEAN foreign exchange markets. The results indicate a positive dependence between the exchange rate returns of CNY and the currencies of ASEAN countries and show the rising power of RMB in the regional currency markets after the B&R Initiative was launched. Besides this, the Malaysian Ringgit proved to be most relevant to the other ASEAN currencies, thus playing an important role in the stability of regional financial markets. Moreover, evidence of tail dependence was found in the returns of three currency pairs after the B&R Initiative, which implies the presence of asymmetric dependence between exchange rates. The results from time-varying C-vine copulas further confirmed the robustness of the results from the static C-vine copulas.

Measuring Dependence Between the USA and the Asian Economies: A Time-varying Copula Approach

2019 ◽  
Vol 20 (4) ◽  
pp. 962-980 ◽  
Author(s):  
Shegorika Rajwani ◽  
Dilip Kumar
Keyword(s):  
Financial Crisis ◽  
Stock Market ◽  
Financial Markets ◽  
Stock Markets ◽  
Global Financial Crisis ◽  
Tail Dependence ◽  
Time Varying ◽  
The Us ◽  
Asian Economies ◽  
Copula Approach

During the past few years, many of the financial markets have gone through devastating effects due to the crisis in one or the other economy of the world. The recent global financial crisis has triggered dramatic movements in various stock markets which may arise from interdependence or contagion between the markets. This article attempts to measure the contagion between the equity markets of Asia and the US stock market. The countries considered in the Asian group are China, India, Indonesia, South Korea, Taiwan, Hong Kong, Malaysia and Japan. Most of the Asian economies have experienced drastic higher volatility and uncertainty in the financial markets. If the markets are contagious, then the investors will be unable to reap benefits through international diversification of the portfolio. In such a case, the policymakers will further frame policies so that they can insulate themselves from inflicting heavy damage from various crises. To achieve our goal, we make use of the time-varying copula approach which helps us to study the joint behaviour of the series based on their marginal distribution. Time-varying copula approach can also capture the non-linear dependence in the series and exhibits a rich pattern of tail behaviour. Our findings support the contagion between the Asian stock markets and the US stock market during the global financial crisis. This article also highlights that the increased tail dependence is an important factor for the contagion between the Asian stock markets and the US market.

Limiting behaviour of the distributions of the maxima of partial sums of certain random walks

1972 ◽  
Vol 9 (3) ◽  
pp. 572-579 ◽  
Author(s):  
D. J. Emery
Keyword(s):  
Distribution Function ◽  
Random Walk ◽  
Asymptotic Property ◽  
Regular Variation ◽  
Domain Of Attraction ◽  
Hitting Times ◽  
Partial Sums ◽  
Symmetric Distributions ◽  
Stable Law ◽  
Limiting Behaviour

It is shown that, under certain conditions, satisfied by stable distributions, symmetric distributions, distributions with zero mean and finite second moment and other distributions, the distribution function of the maxima of successive partial sums of identically distributed random variables has an asymptotic property. This property implies the regular variation of the tail of the distribution of the hitting times of the associated random walk, and hence that these hitting times belong to the domain of attraction of a stable law.

scholarly journals On a conjecture of Seneta on regular variation of truncated moments

2021 ◽  
Vol 109 (123) ◽  
pp. 77-82
Author(s):  
Péter Kevei
Keyword(s):  
Distribution Function ◽  
Relative Stability ◽  
Regular Variation ◽  
Domain Of Attraction ◽  
Random Variable ◽  
Nonnegative Random Variable ◽  
Equivalent Characterization ◽  
Regularly Varying ◽  
Normal Law

We prove that h?(x) = ??x0 y??1F?(y)dy is regularly varying with index ? [0, ?) if and only if V?(x) = ?[0,x] y?dF(y) is regularly varying with the same index, where ? > 0, F(x) is a distribution function of a nonnegative random variable, and F?(x) = 1?F(x). This contains at ? = 0, ?= 1 a result of Rogozin [8] on relative stability, and at ? = 0, ? = 2 a new, equivalent characterization of the domain of attraction of the normal law. For ? = 0 and ? > 0 our result implies a recent conjecture by Seneta [9].

Dependence Structure Analysis and VaR Estimation Based on China’s and International Gold Price: A Copula Approach

2020 ◽  
Vol 19 (01) ◽  
pp. 169-193
Author(s):  
Zhicheng Liang ◽  
Junwei Wang ◽  
Kin Keung Lai
Keyword(s):  
Tail Dependence ◽  
Gold Price ◽  
Dependence Structure ◽  
Copula Models ◽  
Simulation Based ◽  
Copula Approach ◽  
Weighted Portfolio ◽  
Pricing Power ◽  
Gold Producer ◽  
Research Period

Since 2013, China has become the world’s largest gold producer and consumer. To gain the corresponding global pricing power in gold, many actions have been taken by China in recent years, including the International Board at Shanghai Gold Exchange, Shanghai-Hong Kong Gold Connect and Shanghai Gold Fix. Our work studies the dependence structure between China’s and international gold price and examines whether these moves are changing the dependence structure. We use GARCH-copula models to detect the dynamic dependence and tail dependence. The research period is set to contain the Financial Crisis in 2008, the dramatical plunge of gold price in 2013 and a series of black swan events in 2016. The empirical study shows that some event driven dependence structure breaks are statistically insignificant. And the time-varying Symmetrized Joe-Clayton copula is the best copula to model the dependence structure based on AIC value. Finally, an example of applications of this dependence structure is given by estimating the VaR of an equally weighted portfolio with a simulation-based method.

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