Pricing credit derivatives under a correlated regime-switching hazard processes model

Yinghui Dong; Kam Chuen Yuen; Guojing Wang

doi:10.3934/jimo.2016079

Article Contents

2017, Volume 13, Issue 3: 1395-1415. Doi: 10.3934/jimo.2016079

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Pricing credit derivatives under a correlated regime-switching hazard processes model

1.
Department of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou 215009, China
2.
Department of Statistics and Actuarial Science, University of Hong Kong, Pokfulam Road, Hong Kong, China
3.
Center for Financial Engineering and Department of Mathematics, Soochow University, Suzhou 215006, China

* Corresponding author:Yinghui Dong
* Corresponding author:Yinghui Dong

Received: January 31, 2016

Published: September 2017

The authors thank the anonymous referees for valuable comments to improve the earlier version of the paper. The first author is supported by the NSF of Jiangsu Province (Grant No. BK20130260), the NNSF of China (Grant No. 11301369) and Qing Lan Project. The second author is supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. HKU 7057/13P), and the CAE 2013 research grant from the Society of Actuaries -any opinions, finding, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the SOA. The third author is supported by the NNSF of China (Grant No. 11371274).

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Abstract

In this paper, we study the valuation of a single-name credit default swap and a $k$th-to-default basket swap under a correlated regime-switching hazard processes model. We assume that the defaults of all the names are driven by a Markov chain describing the macro-economic conditions and some shock events modelled by a multivariate regime-switching shot noise process. Based on some expressions for the joint Laplace transform of the regime-switching shot noise processes, we give explicit formulas for the spread of a CDS contract and the $k$th-to-default basket swap.

Keywords:

Hazard process,
Markov chain,
$k$th-to-default basket swap,
multivariate regime-switching shot noise process.

Mathematics Subject Classification: Primary: 91B25, 91B70; Secondary: 60J27.

Citation:

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Figure 1. Term structure of $s_1$ with $a=1$

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Figure 2. Impact of $w$ on $s_1$ with $a=1, T=10.$

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Figure 3. Impact of $a$ on $s_1$ with $w=0.01, T=10.$

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Figure 4. Term structure of $s^1$ with $a=1$

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Figure 5. Impact of $w$ on $s^1$ and with $q=0.5, T=10.$

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Figure 6. Impact of $a$ on $s^1$ and with $q=0.5, T=10.$

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