Frontiers of Mathematics in China >

2015 , Vol. 10 >Issue 1: 147 - 183

DOI: https://doi.org/10.1007/s11464-014-0315-4

RESEARCH ARTICLE

Dependence structure between LIBOR rates by copula method

  • Yijun WU 1 ,
  • Zhi ZHENG 2 ,
  • Shulin ZHOU 2 ,
  • Jingping YANG , 1
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  • 1. LMEQF, Department of Financial Mathematics, Center for Statistical Science, Peking University, Beijing 100871, China
  • 2. LMAM, Department of Mathematics, Peking University, Beijing 100871, China

Received date: 27 Feb 2013

Accepted date: 07 May 2013

Published date: 30 Dec 2014

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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Abstract

This paper discusses the correlation structure between London Interbank Offered Rates (LIBOR) by using the copula function. We start from one simplified model of A. Brace, D. Gatarek, and M. Musiela (1997) and find out that the copula function between two LIBOR rates can be expressed as a sum of an infinite series, where the main term is a distribution function with Gaussian copula. Partial differential equation method is used for deriving the copula expansion. Numerical results show that the copula of the LIBOR rates and Gaussian copula are very close in the central region and differ in the tail, and the Gaussian copula approximation to the copula function between the LIBOR rates provides satisfying results in the normal situation.

Key words： London Interbank Offered Rate (LIBOR); copula function; partial differential equation (PDE)

Cite this article

Yijun WU , Zhi ZHENG , Shulin ZHOU , Jingping YANG . Dependence structure between LIBOR rates by copula method[J]. Frontiers of Mathematics in China, 2015 , 10(1) : 147 -183 . DOI: 10.1007/s11464-014-0315-4

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