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Value at Risk of portfolios using copulas

Authors
Byun, KiwoongSong, Seongjoo
Issue Date
1월-2021
Publisher
KOREAN STATISTICAL SOC
Keywords
Value at Risk; portfolio returns; normal inverse Gaussian distribution; copula; vine copula; hierarchical copula
Citation
COMMUNICATIONS FOR STATISTICAL APPLICATIONS AND METHODS, v.28, no.1, pp.59 - 79
Indexed
SCOPUS
KCI
OTHER
Journal Title
COMMUNICATIONS FOR STATISTICAL APPLICATIONS AND METHODS
Volume
28
Number
1
Start Page
59
End Page
79
URI
https://scholar.korea.ac.kr/handle/2021.sw.korea/50303
DOI
10.29220/CSAM.2021.28.1.059
ISSN
2287-7843
Abstract
Value at Risk (VaR) is one of the most common risk management tools in finance. Since a portfolio of several assets, rather than one asset portfolio, is advantageous in the risk diversification for investment, VaR for a portfolio of two or more assets is often used. In such cases, multivariate distributions of asset returns are considered to calculate VaR of the corresponding portfolio. Copulas are one way of generating a multivariate distribution by identifying the dependence structure of asset returns while allowing many different marginal distributions. However, they are used mainly for bivariate distributions and are not widely used in modeling joint distributions for many variables in finance. In this study, we would like to examine the performance of various copulas for high dimensional data and several different dependence structures. This paper compares copulas such as elliptical, vine, and hierarchical copulas in computing the VaR of portfolios to find appropriate copula functions in various dependence structures among asset return distributions. In the simulation studies under various dependence structures and real data analysis, the hierarchical Clayton copula shows the best performance in the VaR calculation using four assets. For marginal distributions of single asset returns, normal inverse Gaussian distribution was used to model asset return distributions, which are generally high-peaked and heavy-tailed.
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Song, Seongjoo
정경대학 (통계학과)
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