scholarly journals Compound Archimedean Copulas

2021 ◽  
Vol 10 (3) ◽  
pp. 126
Author(s):  
Moshe Kelner ◽  
Zinoviy Landsman ◽  
Udi E. Makov
Keyword(s):  
Random Variables ◽  
Copula Function ◽  
Dependence Structure ◽  
Archimedean Copulas ◽  
Copula Functions ◽  
Unique Structure ◽  
The Family ◽  
The Many

The copula function is an effective and elegant tool useful for modeling dependence between random variables. Among the many families of this function, one of the most prominent family of copula is the Archimedean family, which has its unique structure and features. Most of the copula functions in this family have only a single dependence parameter which limits the scope of the dependence structure. In this paper we modify the generator of Archimedean copulas in a way which maintains membership in the family while increasing the number of dependence parameters and, consequently, creating new copulas having more flexible dependence structure.

scholarly journals Fitting Compound Archimedean Copulas to Data for Modeling Electricity Demand

2021 ◽  
Vol 10 (5) ◽  
pp. 20
Author(s):  
Moshe Kelner ◽  
Zinoviy Landsman ◽  
Udi E. Makov
Keyword(s):  
Random Variables ◽  
Electricity Demand ◽  
Archimedean Copula ◽  
Dependence Structure ◽  
Archimedean Copulas ◽  
Copula Functions ◽  
Maximum Daily Temperature ◽  
Multiple Parameter ◽  
Original Family ◽  
Dependence Structures

Modeling dependence between random variables is accomplished effectively by using copula functions. Practitioners often rely on the single parameter Archimedean family which contains a large number of functions, exhibiting a variety of dependence structures. In this work we propose the use of the multiple-parameter compound Archimedean family, which extends the original family and allows more elaborate dependence structures. In particular, we use a copula of this type to model the dependence structure between the minimum daily electricity demand and the maximum daily temperature. It is shown that the compound Archimedean copula enhances the flexibility of the dependence structure and provides a better fit to the data.

ON DEFAULT CORRELATION AND PRICING OF COLLATERALIZED DEBT OBLIGATION BY COPULA FUNCTIONS

2006 ◽  
Vol 05 (03) ◽  
pp. 483-493 ◽  
Author(s):  
PING LI ◽  
HOUSHENG CHEN ◽  
XIAOTIE DENG ◽  
SHUNMING ZHANG
Keyword(s):  
Credit Derivatives ◽  
Copula Function ◽  
Dependence Structure ◽  
Default Correlation ◽  
Specific Kind ◽  
Copula Functions ◽  
Recovery Rates ◽  
Collateralized Debt Obligation ◽  
Collateralized Debt ◽  
Debt Obligation

Default correlation is the key point for the pricing of multi-name credit derivatives. In this paper, we apply copulas to characterize the dependence structure of defaults, determine the joint default distribution, and give the price for a specific kind of multi-name credit derivative — collateralized debt obligation (CDO). We also analyze two important factors influencing the pricing of multi-name credit derivatives, recovery rates and copula function. Finally, we apply Clayton copula, in a numerical example, to simulate default times taking specific underlying recovery rates and average recovery rates, then price the tranches of a given CDO and then analyze the results.

scholarly journals Method to Select Copula Functions

2019 ◽  
Vol 42 (1) ◽  
pp. 61-80 ◽  
Author(s):  
Jorge Alberto Achcar ◽  
Jennyfer Portilla-Yela ◽  
José Rafael Tovar-Cuevas
Keyword(s):  
Statistical Data ◽  
Copula Function ◽  
Good Alternative ◽  
Dependence Structure ◽  
Applied Statistics ◽  
Copula Functions ◽  
Bivariate Data ◽  
Dependence Measure ◽  
Discrimination Methods ◽  
Special Case

Copula functions have been extensively used in applied statistics, becoming a good alternative for modeling the dependence of multivariate data. Each copula function has a different dependence structure. An important issue in these applications is the choice of an appropriate copula function model for each one; thus common classical or Bayesian discrimination methods might not be appropriate for determining the best copula. Considering only the special case of bivariate data, we propose a procedure obtained from a recently introduced dependence measure for selecting an appropriate copula for the statistical data analyses.

scholarly journals Calibrating and Simulating Copula Functions in Financial Applications

2021 ◽  
Vol 7 ◽  
Author(s):  
Annalisa Di Clemente ◽  
Claudio Romano
Keyword(s):  
Financial Market ◽  
Asset Returns ◽  
Copula Function ◽  
Dependence Structure ◽  
Financial Asset ◽  
Financial Assets ◽  
Copula Functions ◽  
Financial Applications ◽  
Different Types ◽  
Financial Asset Returns

Copula functions can be utilized in financial applications to determine the dependence structure of the financial asset returns in the portfolio. Empirical evidence has proved the inadequacy of the multi-normal distribution, traditionally adopted to model the financial asset returns distribution. Copula functions can be employed in a flexible way for building efficient algorithms and to simulate a more adequate distribution of the financial assets. This paper aims to describe some simple statistical procedures currently employed to calibrate the copula functions to the financial market data. Furthermore, we present some useful methods for choosing which copula function better fits the real financial data. Also, some algorithms to simulate random variates from certain types of copula functions are illustrated. Finally, for illustration purposes, the previous procedures described are applied to two Italian equities. In particular, we show how to generate efficient Monte Carlo scenarios of equity log-returns in the bivariate case using different types of copula functions.

Reliability Analysis of Two-Dimensional Series Portal-Framed Bridge System Based on Mixed Copula Functions

2013 ◽  
Vol 574 ◽  
pp. 95-105 ◽  
Author(s):  
Yue Fei Liu ◽  
Da Gang Lu
Keyword(s):  
Failure Modes ◽  
Copula Function ◽  
Monte Carlo Sampling ◽  
Two Dimensional ◽  
Archimedean Copulas ◽  
Copula Functions ◽  
Performance Function ◽  
Mcs Method ◽  
Dimensional Series ◽  
Bridge System

In this paper, several commonly-used Elliptical copulas and Archimedean copulas were introduced, and their application in the correlation analysis were also described in detal. For the two failure modes of two-dimensional series portal-framed bridge system, the performance function values with respect to the failure modes were considered as the analysis variables of the chosen copula functions, and the Baysian copula selection method was applied to select the proper copula functions. And then, the two-dimension mixed copula function was built. Thereinto, the uncertain parameters of copula function were determined with Monte Carlo Sampling (MCS) method, so the numerical modeling of the mixed copula fuction about the failure mode of two-dimensional series portal-framed bridge system was achieved. Finally the reliability of this system was analyzed with the built mixed copula function, and the structural system failure probability was obtained.

scholarly journals Modelling the statistical dependence of rainfall event variables by a trivariate copula function

2011 ◽  
Vol 8 (1) ◽  
pp. 429-481 ◽  
Author(s):  
M. Balistrocchi ◽  
B. Bacchi
Keyword(s):  
Goodness Of Fit ◽  
Random Variables ◽  
Joint Probability ◽  
Copula Function ◽  
Rainfall Event ◽  
Probabilistic Methods ◽  
Statistical Dependence ◽  
Dependence Structure ◽  
Distribution Fitting ◽  
Independent Events

Abstract. In many hydrological models, such as those derived by analytical probabilistic methods, the precipitation stochastic process is represented by means of individual storm random variables which are supposed to be independent of each other. However, several proposals were advanced to develop joint probability distributions able to account for the observed statistical dependence. The traditional technique of the multivariate statistics is nevertheless affected by several drawbacks, whose most evident issue is the unavoidable subordination of the dependence structure assessment to the marginal distribution fitting. Conversely, the copula approach can overcome this limitation, by splitting the problem in two distinct items. Furthermore, goodness-of-fit tests were recently made available and a significant improvement in the function selection reliability has been achieved. Herein a trivariate probability distribution of the rainfall event volume, the wet weather duration and the interevent time is proposed and verified by test statistics with regard to three long time series recorded in different Italian climates. The function was developed by applying a mixing technique to bivariate copulas, which were formerly obtained by analyzing the random variables in pairs. A unique probabilistic model seems to be suitable for representing the dependence structure, despite the sensitivity shown by the dependence parameters towards the threshold utilized in the procedure for extracting the independent events. The joint probability function was finally developed by adopting a Weibull model for the marginal distributions.

MODELING DEPENDENCE BETWEEN LOSS TRIANGLES WITH HIERARCHICAL ARCHIMEDEAN COPULAS

2015 ◽  
Vol 45 (3) ◽  
pp. 577-599 ◽  
Author(s):  
Anas Abdallah ◽  
Jean-Philippe Boucher ◽  
Hélène Cossette
Keyword(s):  
Life Insurance ◽  
Bootstrap Method ◽  
Dependence Structure ◽  
Insurance Company ◽  
Archimedean Copulas ◽  
Life Insurance Company ◽  
Critical Problems ◽  
Intuitive Interpretation ◽  
Property Casualty

AbstractOne of the most critical problems in property/casualty insurance is to determine an appropriate reserve for incurred but unpaid losses. These provisions generally comprise most of the liabilities of a non-life insurance company. The global provisions are often determined under an assumption of independence between the lines of business. Recently, Shi and Frees (2011) proposed to put dependence between lines of business with a copula that captures dependence between two cells of two different runoff triangles. In this paper, we propose to generalize this model in two steps. First, by using an idea proposed by Barnett and Zehnwirth (1998), we will suppose a dependence between all the observations that belong to the same calendar year (CY) for each line of business. Thereafter, we will then suppose another dependence structure that links the CYs of different lines of business. This model is done by using hierarchical Archimedean copulas. We show that the model provides more flexibility than existing models, and offers a better, more realistic and more intuitive interpretation of the dependence between the lines of business. For illustration, the model is applied to a dataset from a major US property-casualty insurer, where a bootstrap method is proposed to estimate the distribution of the reserve.

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.

Two primitive trematopid amphibians (Temnospondyli, Dissorophoidea) from the Upper Carboniferous of the Czech Republic

2018 ◽  
Vol 109 (1-2) ◽  
pp. 201-223 ◽  
Author(s):  
Andrew R. MILNER
Keyword(s):  
Czech Republic ◽  
The Czech Republic ◽  
Upper Carboniferous ◽  
Incertae Sedis ◽  
Terminal Form ◽  
The Family ◽  
Nasal Region ◽  
The Many

ABSTRACTSpecimens of trematopid amphibians from the Asturian (Upper Carboniferous) of Nýřany, Czech Republic, are redescribed as two taxa, namely Mordex calliprepes Steen and Mattauschia (gen. nov) laticeps Fritsch. Mordex calliprepes is represented by a single post-metamorphic specimen and has the diagnostic trematopid characters of the nasal region. Mattauschia laticeps is represented by one adult partial skull and mandible plus some fragments and two small post-metamorphic specimens including the species name-bearer. It has the trematopid-type modified lacrimal and a large but oval naris and appears to be the most primitive trematopid yet described. The stratigraphically sequential large trematopids Mattauschia, Fedexia, Ecolsonia and Acheloma show progressive acquisition of the derived features that characterise the terminal form Acheloma.Mordex has a combination of primitive and derived characters and its position within the family is less clear. The many ‘branchiosaurs' in the Nýřany assemblage include specimens that could be larvae of both Mordex and Mattauschia but certain attribution is not possible and they are assigned to Olsoniformes incertae sedis. Mordex and Mattauschia appear to be terrestrial exotic elements in the Nýřany tetrapod assemblage, but with possible larvae in the lake assemblage. Representatives of at least four Palaeozoic dissorophoid families were present in late Middle Pennsylvanian/Asturian strata implying diversification of the Dissorophoidea prior to this time.

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