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.

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 Dependence Measure of Daily versus Weekly Returns

2018 ◽  
Vol 7 (3.20) ◽  
pp. 329
Author(s):  
Nurul Hanis Aminuddin ◽  
Ruzanna Ab Razak ◽  
Noriszura Ismail
Keyword(s):  
Portfolio Management ◽  
Composite Index ◽  
Dependence Structure ◽  
Frequency Data ◽  
Kuala Lumpur ◽  
Bivariate Data ◽  
Dependence Measure ◽  
Daily Data ◽  
Copula Method ◽  
Daily Returns

The copula method has been popular among researchers, especially in measuring the overall dependence and extreme dependence of multivariate data. Many copula studies have been focusing on examining the correlation of bivariate daily, monthly or weekly returns to explain the co-movement between financial markets and possible financial implications on portfolio management. Differently from past studies, this paper investigates whether different frequency of bivariate data (daily and weekly returns) possesses different dependence structures. The data from Kuala Lumpur Composite Index (KLCI) and Bursa Malaysia Hijrah Shariah Index (FBMHS) for the sample period of 2008 Q1 to 2017 Q1 are used for studying the dependency. The findings from this study reveal that both daily and weekly bivariate returns have the same dependence structure but different degree of dependence. Bivariate weekly returns showed stronger dependence compared to bivariate daily returns. This paper also highlights the statistical properties of weekly and daily data. The evidence from this research draws inferences for further study that lower frequency data such as monthly or quarterly returns data may have higher degree of dependence while higher frequency data may have lower degree of dependence and different copula structure.

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 Use of copula functions for the reliability of series systems

2015 ◽  
Vol 32 (6) ◽  
pp. 617-634 ◽  
Author(s):  
Jorge Alberto Achcar ◽  
Fernando Antonio Moala
Keyword(s):  
Simulated Data ◽  
Reliability Function ◽  
Good Alternative ◽  
Bivariate Distribution ◽  
Parametric Models ◽  
Dependence Structure ◽  
Series System ◽  
Copula Functions ◽  
Content Type ◽  
Series Systems

Purpose – The purpose of this paper is to provide a new method to estimate the reliability of series system by using copula functions. This problem is of great interest in industrial and engineering applications. Design/methodology/approach – The authors introduce copula functions and consider a Bayesian analysis for the proposed models with application to the simulated data. Findings – The use of copula functions for modeling the bivariate distribution could be a good alternative to estimate the reliability of a two components series system. From the results of this study, the authors observe that they get accurate Bayesian inferences for the reliability function considering large samples sizes. The Bayesian parametric models proposed also allow the assessment of system reliability for multicomponent systems simultaneously. Originality/value – Usually, the studies of systems reliability engineering assume independence among the component lifetimes. In the approach the authors consider a dependence structure. Using standard classical inference methods based on asymptotical normality of the maximum likelihood estimators for the parameters the authors could have great computational difficulties and possibly, not accurate inference results, which there is not found in the approach.

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.

scholarly journals A Copula-Based Framework for Studying Intergenerational Income Mobility

2021 ◽  
Author(s):  
Anning Hu ◽  
Zhipeng Zhou
Keyword(s):  
Analytical Framework ◽  
Dependence Structure ◽  
Income Mobility ◽  
Mobility Patterns ◽  
Copula Functions ◽  
Intergenerational Income Mobility ◽  
Intergroup Comparison ◽  
Copula Density ◽  
Von Mises ◽  
Morphological Patterns

The sociological analysis of the mobility tables enhances the examination of the circulation mobility and helps one reveal the nuanced morphological patterns of mobility. In contrast, the economic analysis based on the measure of elasticity provides a handy way of covariate conditioning and statistically testing the similarities of mobility patterns across groups. In this article, we argue that the distinct methodological merits of these two approaches can be equipped by adopting a more comprehensive analytical framework using the copula functions: (1) The copula functions concern the dependence structure that is independent from the margins, which enable scholars to focus on the relative mobility; (2) The copula density, estimated either parametrically or non-parametrically, reveals the nuanced morphological mobility patterns; (3) By residualizing the marginal variables, the detected mobility pattern can be interpreted in a stronger causal sense; and (4) the Cramér–von Mises Test offers an easy-to-use statistic to conduct intergroup comparison of mobility patterns. The copula-based framework is illustrated by investigating the income mobility between 1978 and 2017 in the U.S., using the National Longitudinal Survey of Youth 1979 (NLSY79).

scholarly journals Investigating students’ use of official statistical data

2019 ◽  
Vol 1 (1) ◽  
pp. 329-342
Author(s):  
Constanța Mihăescu ◽  
Adrian Oţoiu ◽  
Alina Profiroiu ◽  
Ileana Niculescu-Aron
Keyword(s):  
Statistical Data ◽  
Real Life ◽  
Data Sources ◽  
Applied Statistics ◽  
Science Students ◽  
Statistical Education ◽  
Custom Made ◽  
Problems And Solutions ◽  
Life Issues ◽  
Official Data

Abstract This paper presents the perceptions of social science students about the use of official statistical data, in the context of active learning of Statistics, and other topics related to Applied Statistics. In order to make these courses more attractive, and to challenge and stimulate statistical education, our students work on projects in which they use official statistical data to explore practical, real-life issues. Their attitudes and perceptions regarding official statistical data sources are very important, both for acquisition of statistical analysis skills, essential for their future professional life, and for improvement of the official data sources. Therefore, we conducted a custom-made survey among students from Romanian higher education institutions (HEIs) and gathered a database with 334 responses, which allowed us to identify the main characteristics, problems and solutions concerning the use of statistical official data sources by university students.

scholarly journals Drought Risk Analysis in the Eastern Cape Province of South Africa: The Copula Lens

Water ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1938 ◽  
Author(s):  
Christina M. Botai ◽  
Joel O. Botai ◽  
Abiodun M. Adeola ◽  
Jaco P. de Wit ◽  
Katlego P. Ncongwane ◽  
...  
Keyword(s):  
South Africa ◽  
Gaussian Copula ◽  
Dependence Structure ◽  
Drought Risk ◽  
Eastern Cape Province ◽  
Return Periods ◽  
Eastern Cape ◽  
Copula Functions ◽  
Drought Duration ◽  
Drought Duration And Severity

This research study was carried out to investigate the characteristics of drought based on the joint distribution of two dependent variables, the duration and severity, in the Eastern Cape Province, South Africa. The drought variables were computed from the Standardized Precipitation Index for 6- and 12-month accumulation period (hereafter SPI-6 and SPI-12) time series calculated from the monthly rainfall data spanning the last five decades. In this context, the characteristics of climatological drought duration and severity were based on multivariate copula analysis. Five copula functions (from the Archimedean and Elliptical families) were selected and fitted to the drought duration and severity series in order to assess the dependency measure of the two variables. In addition, Joe and Gaussian copula functions were considered and fitted to the drought duration and severity to assess the joint return periods for the dual and cooperative cases. The results indicate that the dependency measure of drought duration and severity are best described by Tawn copula families. The dependence structure results suggest that the study area exhibited low probability of drought duration and high probability of drought severity. Furthermore, the multivariate return period for the dual case is found to be always longer across all the selected univariate return periods. Based on multivariate analysis, the study area (particularly Buffalo City, OR Tambo and Alfred Zoo regions) is determined to have higher/lower risks in terms of the conjunctive/cooperative multivariate drought risk (copula) probability index. The results of the present study could contribute towards policy and decision making through e.g., formulation of the forward-looking contingent plans for sustainable management of water resources and the consequent applications in the preparedness for and adaptation to the drought risks in the water-linked sectors of the economy.

On the dependence structure of hitting times of univariate processes

1988 ◽  
Vol 25 (02) ◽  
pp. 355-362 ◽  
Author(s):  
Nader Ebrahimi ◽  
T. Ramalingam
Keyword(s):  
Brownian Motion ◽  
Structural Properties ◽  
Hitting Times ◽  
Dependence Structure ◽  
Special Case ◽  
New Better Than Used ◽  
Better Than

Some concepts of dependence have recently been introduced by Ebrahimi (1987) to explore the structural properties of the hitting times of bivariate processes. In this framework, the special case of univariate processes has curious features. New properties are derived for this case. Some applications to sequential inference and inequalities for Brownian motion and new better than used (NBU) processes are also provided.

scholarly journals Bayesian Estimation of Archimedean Copula-Based SUR Quantile Models

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Nachatchapong Kaewsompong ◽  
Paravee Maneejuk ◽  
Woraphon Yamaka
Keyword(s):  
Bayesian Estimation ◽  
Bayesian Method ◽  
Real Data ◽  
Copula Function ◽  
Dependence Structure ◽  
Simulation Studies ◽  
Multivariate Normal ◽  
Empirical Comparison ◽  
Proposed Model ◽  
Conventional Models

We propose a high-dimensional copula to model the dependence structure of the seemingly unrelated quantile regression. As the conventional model faces with the strong assumption of the multivariate normal distribution and the linear dependence structure, thus, we apply the multivariate exchangeable copula function to relax this assumption. As there are many parameters to be estimated, we consider the Bayesian Markov chain Monte Carlo approach to estimate the parameter interests in the model. Four simulation studies are conducted to assess the performance of our proposed model and Bayesian estimation. Satisfactory results from simulation studies are obtained suggesting the good performance and reliability of the Bayesian method used in our proposed model. The real data analysis is also provided, and the empirical comparison indicates our proposed model outperforms the conventional models in all considered quantile levels.

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