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AN ANALYTICAL APPROXIMATION FORMULA FOR THE PRICING OF CREDIT DEFAULT SWAPS WITH REGIME SWITCHING

Part of: Mathematical finance

Published online by Cambridge University Press:  02 September 2021

XIN-JIANG HE Open the ORCID record for XIN-JIANG HE [Opens in a new window]  and
SHA LIN Open the ORCID record for SHA LIN [Opens in a new window]
XIN-JIANG HE
Affiliation:
School of Economics, Zhejiang University of Technology, Hangzhou, China; e-mail: xinjiang@zjut.edu.cn.
SHA LIN*
Affiliation:
School of Finance, Zhejiang Gongshang University, Hangzhou, China
*
e-mail: linsha@mail.zjgsu.edu.cn.
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Abstract

We derive an analytical approximation for the price of a credit default swap (CDS) contract under a regime-switching Black–Scholes model. To achieve this, we first derive a general formula for the CDS price, and establish the relationship between the unknown no-default probability and the price of a down-and-out binary option written on the same reference asset. Then we present a two-step procedure: the first step assumes that all the future information of the Markov chain is known at the current time and presents an approximation for the conditional price under a time-dependent Black–Scholes model, based on which the second step derives the target option pricing formula written in a Fourier cosine series. The efficiency and accuracy of the newly derived formula are demonstrated through numerical experiments.

Keywords

analytical approximationcredit default swapregime switchingFourier cosine series

MSC classification

Primary: 91G20: Derivative securities
Type
Research Article
Information
The ANZIAM Journal , Volume 63 , Issue 2 , April 2021 , pp. 143 - 162
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Copyright
© Australian Mathematical Society 2021

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