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




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


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.


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.





Special Issue for Financial Mathematics, Probability and Statistics