scholarly journals Conditional tail independence in Archimedean copula models

2019 ◽  
Vol 56 (3) ◽  
pp. 858-869
Author(s):  
Michael Falk ◽  
Simone A. Padoan ◽  
Florian Wisheckel
Keyword(s):  
Distribution Function ◽  
Random Vector ◽  
Mild Condition ◽  
Conditional Distribution ◽  
Archimedean Copula ◽  
Tail Behavior ◽  
Copula Models ◽  
Generator Function

AbstractConsider a random vector $\textbf{U}$ whose distribution function coincides in its upper tail with that of an Archimedean copula. We report the fact that the conditional distribution of $\textbf{U}$ , conditional on one of its components, has under a mild condition on the generator function independent upper tails, no matter what the unconditional tail behavior is. This finding is extended to Archimax copulas.

A new bivariate Archimedean copula with application to the evaluation of VaR

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Cigdem Topcu Guloksuz ◽  
Pranesh Kumar
Keyword(s):  
Monte Carlo ◽  
Value At Risk ◽  
Simulation Method ◽  
Archimedean Copula ◽  
Dependence Structure ◽  
General Motor ◽  
Copula Models ◽  
Bivariate Normal ◽  
Mc Simulation ◽  
Generator Function

AbstractIn this paper, a new generator function is proposed and based on this function a new Archimedean copula is introduced. The new Archimedean copula along with three representatives of Archimedean copula family which are Clayton, Gumbel and Frank copulas are considered as models for the dependence structure between the returns of two stocks. These copula models are used to simulate daily log-returns based on Monte Carlo (MC) method for calculating value at risk (VaR) of the financial portfolio which consists of two market indices, Ford and General Motor Company. The results are compared with the traditional MC simulation method with the bivariate normal assumption as a model of the returns. Based on the backtesting results, describing the dependence structure between the returns by the proposed Archimedean copula provides more reliable results over the considered models in calculating VaR of the studied portfolio.

scholarly journals Asymptotic normality of conditional distribution estimation in the single index model

2017 ◽  
Vol 9 (1) ◽  
pp. 162-175
Author(s):  
Diaa Eddine Hamdaoui ◽  
Amina Angelika Bouchentouf ◽  
Abbes Rabhi ◽  
Toufik Guendouzi
Keyword(s):  
Distribution Function ◽  
Confidence Interval ◽  
Asymptotic Normality ◽  
Conditional Distribution ◽  
Conditional Distribution Function ◽  
Single Index ◽  
Index Model ◽  
Single Index Model ◽  
Distribution Estimation

AbstractThis paper deals with the estimation of conditional distribution function based on the single-index model. The asymptotic normality of the conditional distribution estimator is established. Moreover, as an application, the asymptotic (1 − γ) confidence interval of the conditional distribution function is given for 0 < γ < 1.

scholarly journals Multiperiod conditional distribution functions for conditionally normal GARCH(1, 1) models

2005 ◽  
Vol 42 (02) ◽  
pp. 426-445
Author(s):  
Raymond Brummelhuis ◽  
Dominique Guégan
Keyword(s):  
Conditional Probability ◽  
Conditional Distribution ◽  
Probability Distributions ◽  
Random Variables ◽  
Distribution Functions ◽  
Tail Behavior ◽  
Asymptotic Tail

We study the asymptotic tail behavior of the conditional probability distributions of r t+k and r t+1+⋯+r t+k when (r t ) t∈ℕ is a GARCH(1, 1) process. As an application, we examine the relation between the extreme lower quantiles of these random variables.

scholarly journals Tail Approximations for Sums of Dependent Regularly Varying Random Variables Under Archimedean Copula Models

2018 ◽  
Vol 21 (2) ◽  
pp. 461-490 ◽  
Author(s):  
Hélène Cossette ◽  
Etienne Marceau ◽  
Quang Huy Nguyen ◽  
Christian Y. Robert
Keyword(s):  
Random Variables ◽  
Archimedean Copula ◽  
Copula Models ◽  
Regularly Varying

scholarly journals One- versus multi-component regular variation and extremes of Markov trees

2020 ◽  
Vol 52 (3) ◽  
pp. 855-878
Author(s):  
Johan Segers
Keyword(s):  
Time Series ◽  
Random Vector ◽  
Regular Variation ◽  
Conditional Independence ◽  
Conditional Distribution ◽  
The Self ◽  
Stationary Time Series ◽  
Markov Tree ◽  
Regularly Varying ◽  
Coupled Random Walks

AbstractA Markov tree is a random vector indexed by the nodes of a tree whose distribution is determined by the distributions of pairs of neighbouring variables and a list of conditional independence relations. Upon an assumption on the tails of the Markov kernels associated to these pairs, the conditional distribution of the self-normalized random vector when the variable at the root of the tree tends to infinity converges weakly to a random vector of coupled random walks called a tail tree. If, in addition, the conditioning variable has a regularly varying tail, the Markov tree satisfies a form of one-component regular variation. Changing the location of the root, that is, changing the conditioning variable, yields a different tail tree. When the tails of the marginal distributions of the conditioning variables are balanced, these tail trees are connected by a formula that generalizes the time change formula for regularly varying stationary time series. The formula is most easily understood when the various one-component regular variation statements are tied up into a single multi-component statement. The theory of multi-component regular variation is worked out for general random vectors, not necessarily Markov trees, with an eye towards other models, graphical or otherwise.

Filtering equations for the conditional law of residual lifetimes from a heterogeneous population

2000 ◽  
Vol 37 (3) ◽  
pp. 823-834 ◽  
Author(s):  
A. Gerardi ◽  
F. Spizzichino ◽  
B. Torti
Keyword(s):  
Random Vector ◽  
Probabilistic Model ◽  
Conditional Distribution ◽  
Heterogeneous Population ◽  
Main Assumption ◽  
Stochastic Filtering ◽  
Occupation Numbers ◽  
History Of ◽  
Residual Lifetimes

We consider a probabilistic model of a heterogeneous population P subdivided into homogeneous sub-cohorts. A main assumption is that the frailties give rise to a discrete, exchangeable random vector. We put ourselves in the framework of stochastic filtering to derive the conditional distribution of residual lifetimes of surviving individuals, given an observed history of failures and survivals. As a main feature of our approach, this study is based on the analysis of behaviour of the vector of ‘occupation numbers’.

scholarly journals Generalized contact distributions of inhomogeneous Boolean models

2002 ◽  
Vol 34 (01) ◽  
pp. 21-47 ◽  
Author(s):  
Daniel Hug ◽  
Günter Last ◽  
Wolfgang Weil
Keyword(s):  
Convex Body ◽  
Large Class ◽  
Random Vector ◽  
Boundary Point ◽  
Conditional Distribution ◽  
Boolean Model ◽  
Spatial Density ◽  
Boolean Models ◽  
Grain Distribution ◽  
Contact Distribution

The main purpose of this work is to study and apply generalized contact distributions of (inhomogeneous) Boolean models Z with values in the extended convex ring. Given a convex body L ⊂ ℝ d and a gauge body B ⊂ ℝ d , such a generalized contact distribution is the conditional distribution of the random vector (d B (L,Z),u B (L,Z),p B (L,Z),l B (L,Z)) given that Z∩L = ∅, where Z is a Boolean model, d B (L,Z) is the distance of L from Z with respect to B, p B (L,Z) is the boundary point in L realizing this distance (if it exists uniquely), u B (L,Z) is the corresponding boundary point of B (if it exists uniquely) and l B (L,·) may be taken from a large class of locally defined functionals. In particular, we pursue the question of the extent to which the spatial density and the grain distribution underlying an inhomogeneous Boolean model Z are determined by the generalized contact distributions of Z.

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