An analytical approximation formula for the pricing of credit default swaps with regime switching

Xin-Jiang He; Sha Lin

doi:10.21914/anziamj.v63.15290

Authors

Xin-Jiang He Zhejiang University of Technology https://orcid.org/0000-0003-1429-5463
Sha Lin Zhejiang Gongshang University https://orcid.org/0000-0003-1692-8711

DOI:

https://doi.org/10.21914/anziamj.v63.15290

Keywords:

analytical approximation, credit default swap, regime switching, Fourier cosine series

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.

doi:10.1017/S1446181121000274

Author Biographies

Xin-Jiang He, Zhejiang University of Technology

School of Economics, Zhejiang University of Technology, Hangzhou, China.

Sha Lin, Zhejiang Gongshang University

School of Finance, Zhejiang Gongshang University, Hangzhou, China.