Frontiers of Mathematics in China >

2016 , Vol. 11 >Issue 6: 1419 - 1450

DOI: https://doi.org/10.1007/s11464-016-0537-8

RESEARCH ARTICLE

Pricing kthrealization derivatives and collateralized debt obligation with multivariate Fréchet copula

  • Zhijin CHEN 1 ,
  • Jingping YANG , 2 ,
  • Xiaoqian WANG 3
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  • 1. Department of Financial Mathematics, Peking University, Beijing 100871, China
  • 2. LMEQF, Department of Financial Mathematics, Center for Statistical Science, Peking University, Beijing 100871, China
  • 3. School of Mathematical Sciences, Institute of Mathematics, Institute of Finance and Statistics, Nanjing Normal University, Nanjing 210023, China

Received date: 08 Jun 2014

Accepted date: 09 Mar 2016

Published date: 18 Oct 2016

Copyright

2016 Higher Education Press and Springer-Verlag Berlin Heidelberg
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Abstract

Copula method has been widely applied to model the correlation among underlying assets in financial market. In this paper, we propose to use the multivariate Fréchet copula family presented in J. P. Yang et al. [Insurance Math. Econom., 2009, 45: 139–147] to price multivariate financial instruments whose payoffs depend on the kth realization of the underlying assets and collateralized debt obligation (CDO). The advantage of the multivariate Fréchet copula is discussed. Empirical study shows that such copula family gives a better fitting to CDO’s market price than Gaussian copula for some derivatives.

Key words： Multivariate Fréchet copula; kth realization derivative; order statistics; collateralized debt obligation (CDO);

Cite this article

Zhijin CHEN , Jingping YANG , Xiaoqian WANG . Pricing kthrealization derivatives and collateralized debt obligation with multivariate Fréchet copula[J]. Frontiers of Mathematics in China, 2016 , 11(6) : 1419 -1450 . DOI: 10.1007/s11464-016-0537-8

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