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Sustainability 2017, 9(10), 1762; doi:10.3390/su9101762

Risk Measurement and Risk Modelling Using Applications of Vine Copulas

1
School of Mathenatics and Statistics, Sydney University, Sydney, NSW 2006, Australia
2
School of Business and Law, Edith Cowan University, Joondalup, WA 6027, Australia
3
Department of Quantitative Finance, National Tsing Hua University, 30013 Hsinchu City, Taiwan
4
Discipline of Business Analytics, University of Sydney Business School, Sydney, NSW 2006, Australia
5
Econometric Institute, Erasmus School of Economics, Erasmus University Rotterdam, 3062 PA Rotterdam, The Netherlands
6
Department of Quantitative Economics, Complutense University of Madrid, 28040 Madrid, Spain
7
Institute of Advanced Sciences, Yokohama National University, 240-8501 Yokohama, Japan
*
Author to whom correspondence should be addressed.
Received: 8 August 2017 / Revised: 10 September 2017 / Accepted: 13 September 2017 / Published: 29 September 2017
(This article belongs to the Special Issue Risk Measures with Applications in Finance and Economics)
View Full-Text   |   Download PDF [1257 KB, uploaded 29 September 2017]   |  

Abstract

This paper features an application of Regular Vine copulas which are a novel and recently developed statistical and mathematical tool which can be applied in the assessment of composite financial risk. Copula-based dependence modelling is a popular tool in financial applications, but is usually applied to pairs of securities. By contrast, Vine copulas provide greater flexibility and permit the modelling of complex dependency patterns using the rich variety of bivariate copulas which may be arranged and analysed in a tree structure to explore multiple dependencies. The paper features the use of Regular Vine copulas in an analysis of the co-dependencies of 10 major European Stock Markets, as represented by individual market indices and the composite STOXX 50 index. The sample runs from 2005 to the end of 2013 to permit an exploration of how correlations change indifferent economic circumstances using three different sample periods: pre-GFC (January 2005–July 2007), GFC (July 2007– September 2009), and post-GFC periods (September 2009–December 2013). The empirical results suggest that the dependencies change in a complex manner, and are subject to change in different economic circumstances. One of the attractions of this approach to risk modelling is the flexibility in the choice of distributions used to model co-dependencies. The practical application of Regular Vine metrics is demonstrated via an example of the calculation of the VaR of a portfolio made up of the indices. View Full-Text
Keywords: regular vine copulas; tree structures; co-dependence modelling; European stock markets regular vine copulas; tree structures; co-dependence modelling; European stock markets
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Allen, D.E.; McAleer, M.; Singh, A.K. Risk Measurement and Risk Modelling Using Applications of Vine Copulas. Sustainability 2017, 9, 1762.

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