Sains Malaysiana 40(8)(2011): 927–935

Tail Dependence Estimate in Financial Market Risk Management:

Clayton-Gumbel Copula Approach

(Nilai Kebersandaran Ekor Bagi Anggaran Dalam Pengurusan Risiko Pasaran

Kewangan: Pendekatan Clayton-Gumbel Copula)

A.     Ahmed Shamiri*, N.A. Hamzah & A. Pirmoradian

Institute of Mathematical Sciences, Faculty of Science, Univeristy of Malaya

50603 Kuala Lumpur, Malaysia

Diserahkan: 20 Mei 2010 /Diterima: 10 November 2010

ABSTRACT

This paper focuses on measuring risk due to extreme events going beyond the multivariate normal distribution of joint returns. The concept of tail dependence has been found useful as a tool to describe dependence between extreme data in finance. Specifically, we adopted a multivariate Copula-EGARCH approach in order to investigate the presence of conditional dependence between international financial markets. In addition, we proposed a mixed Clayton-Gumbel copula with estimators for measuring both, the upper and lower tail dependence. The results showed significant dependence for Singapore and Malaysia as well as for Singapore and US, while the dependence for Malaysia and US was relatively weak.

Keywords: Copulas; EGARCH model; risk measures; tail dependence

ABSTRAK

Kajian ini menumpu kepada pengukuran risiko yang disebabkan oleh kejadian ekstrim yang berlaku di luar batasan taburan multivariat normal bagi pulangan bercantum. Konsep kebersandaran ekor telah didapati berguna sebagai alat bagi menerangkan kebersandaran di kalangan data ekstrim dalam kewangan. Secara spesifik, kami mengadaptasi pendekatan multivariate Copula-EGARCH untuk mengkaji kewujudan kebersandaran bersyarat antara pasaran kewangan antarabangsa. Kami juga mencadangkan campuran copula Clayton-Gumbel dengan penganggar bagi mengukur kedua-dua had atas dan bawah ekor kebersandaran. Keputusan kajian ini menunjukkan kebersandaran yang signifikan antara Singapura-Malaysia serta Singapura-Amerika Syarikat, manakala kebersandaran untuk Malaysia-Amerika Syarikat adalah lemah secara relatif.

Kata kunci: Copula; kebersandaran ekor; model EGARCH; ukuran risiko

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*Pengarang untuk surat-menyurat; email: ahmed_shamir@um.edu.my