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Credit default swap pricing with counterparty risk in a reduced form model with a common jump process

Published online by Cambridge University Press:  22 February 2022

Yu Chen  and
Yu Xing Open the ORCID record for Yu Xing [Opens in a new window]
Yu Chen
Affiliation:
Department of Applied Mathematics, Nanjing University of Science & Technology, Nanjing 210094, China
Yu Xing
Affiliation:
School of Finance, Nanjing Audit University, Nanjing 211815, China Key Laboratory of Financial Engineering, Nanjing Audit University, Nanjing 211815, China. E-mail: xingyu5901@hotmail.com
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Abstract

In this paper, we study the credit default swap (CDS) pricing with counterparty risk in a reduced form model. The default jump intensities of the reference firm and counterparty are both assumed to follow the mean-reverting CIR processes with independent jumps respectively and a common jump. The approximate closed-form solutions of the joint survival probability density and the probability density of the first default can be obtained by using the PDE method. Then with the expressions of the probability densities, we can get the formula for the CDS price with counterparty risk in a reduced form model with a common jump. In the numerical analysis part, we find that the default of the reference asset has a greater impact on the CDS price than that of the default of counterparty after introducing the common jump process.

Keywords

CDS pricingCommon jumpCounterparty risk
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 37 , Issue 1 , January 2023 , pp. 275 - 293
Copyright
Copyright © The Author(s), 2022. Published by Cambridge University Press

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