Distorted Mix Method for constructing copulas with tail dependence |
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| Institution: | 1. Department of Financial Mathematics, Peking University, Beijing 100871, China;2. Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong;3. LMEQF, Department of Financial Mathematics, Peking University, Beijing 100871, China;1. Department of Mathematics, Northwest University, Xi’an 710069, PR China;2. Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023, PR China;1. Chair for Computation in Engineering, Technische Universität München, Germany;2. Institute for Advanced Study, Technische Universität München, Germany;3. Dipartimento di Ingegneria Civile e Architettura, Università degli Studi di Pavia, Italy;1. Department of Statistics, Inha University, 235 Yonghyun-Dong, Nam-Gu, Incheon 402-751, Republic of Korea;2. Department of Statistics, Ewha Womans University, 11-1 Daehyun-Dong, Seodaemun-Gu, Seoul 120-750, Republic of Korea |
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| Abstract: | This paper introduces a method for constructing copula functions by combining the ideas of distortion and convex sum, named Distorted Mix Method. The method mixes different copulas with distorted margins to construct new copula functions, and it enables us to model the dependence structure of risks by handling the central and tail parts separately. By applying the method we can modify the tail dependence of a given copula to any desired level measured by tail dependence function and tail dependence coefficients of marginal distributions. As an application, a tight bound for asymptotic Value-at-Risk of order statistics is obtained by using the method. An empirical study shows that copulas constructed by this method fit the empirical data of SPX 500 Index and FTSE 100 Index very well in both central and tail parts. |
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| Keywords: | Copula Distorted Mix Method Distortion function Tail dependence coefficient Tail dependence function |
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