Finite-time survival probability and credit default swaps pricing under geometric Lévy markets

Xuemiao Hao; Xuan Li; Yasutaka Shimizu

doi:10.1016/j.insmatheco.2013.04.003

Finite-time survival probability and credit default swaps pricing under geometric Lévy markets

Xuemiao Hao^*, Xuan Li, Yasutaka Shimizu

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

We study the first-passage time over a fixed threshold for a pure-jump subordinator with negative drift. We obtain a closed-form formula for its survival function in terms of marginal density functions of the subordinator. We then use this formula to calculate finite-time survival probabilities in a structural model for credit risk, and thus obtain a closed-form pricing formula for a single-name credit default swap (CDS). This pricing formula is well calibrated on market CDS quotes. In particular, it explains why the par CDS credit spread is not negligible when the maturity becomes short.

Original language	English
Pages (from-to)	14-23
Number of pages	10
Journal	Insurance: Mathematics and Economics
Volume	53
Issue number	1
DOIs	https://doi.org/10.1016/j.insmatheco.2013.04.003
Publication status	Published - 2013 Jul
Externally published	Yes

Keywords

Credit default swap
Finite-time survival probability
First-passage time
Lévy process
Structural model

ASJC Scopus subject areas

Statistics and Probability
Economics and Econometrics
Statistics, Probability and Uncertainty

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10.1016/j.insmatheco.2013.04.003

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@article{e2b8f92d3eb14ac09fece83d834d8175,

title = "Finite-time survival probability and credit default swaps pricing under geometric L{\'e}vy markets",

abstract = "We study the first-passage time over a fixed threshold for a pure-jump subordinator with negative drift. We obtain a closed-form formula for its survival function in terms of marginal density functions of the subordinator. We then use this formula to calculate finite-time survival probabilities in a structural model for credit risk, and thus obtain a closed-form pricing formula for a single-name credit default swap (CDS). This pricing formula is well calibrated on market CDS quotes. In particular, it explains why the par CDS credit spread is not negligible when the maturity becomes short.",

keywords = "Credit default swap, Finite-time survival probability, First-passage time, L{\'e}vy process, Structural model",

author = "Xuemiao Hao and Xuan Li and Yasutaka Shimizu",

note = "Funding Information: The authors would like to thank the anonymous reviewer for a number of valuable comments, which helped us improve the paper greatly. XH acknowledges support of the Natural Sciences and Engineering Research Council of Canada (grant no. 386552-2010 ) and the Start-up Research Fund from the University of Manitoba . XL acknowledges support of the Start-up Funds from the University of Minnesota Duluth . YS acknowledges support of JSPS KAKENHI grant no. 24740061 and JST CREST . ",

year = "2013",

month = jul,

doi = "10.1016/j.insmatheco.2013.04.003",

language = "English",

volume = "53",

pages = "14--23",

journal = "Insurance: Mathematics and Economics",

issn = "0167-6687",

publisher = "Elsevier",

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TY - JOUR

T1 - Finite-time survival probability and credit default swaps pricing under geometric Lévy markets

AU - Hao, Xuemiao

AU - Li, Xuan

AU - Shimizu, Yasutaka

N1 - Funding Information: The authors would like to thank the anonymous reviewer for a number of valuable comments, which helped us improve the paper greatly. XH acknowledges support of the Natural Sciences and Engineering Research Council of Canada (grant no. 386552-2010 ) and the Start-up Research Fund from the University of Manitoba . XL acknowledges support of the Start-up Funds from the University of Minnesota Duluth . YS acknowledges support of JSPS KAKENHI grant no. 24740061 and JST CREST .

PY - 2013/7

Y1 - 2013/7

N2 - We study the first-passage time over a fixed threshold for a pure-jump subordinator with negative drift. We obtain a closed-form formula for its survival function in terms of marginal density functions of the subordinator. We then use this formula to calculate finite-time survival probabilities in a structural model for credit risk, and thus obtain a closed-form pricing formula for a single-name credit default swap (CDS). This pricing formula is well calibrated on market CDS quotes. In particular, it explains why the par CDS credit spread is not negligible when the maturity becomes short.

AB - We study the first-passage time over a fixed threshold for a pure-jump subordinator with negative drift. We obtain a closed-form formula for its survival function in terms of marginal density functions of the subordinator. We then use this formula to calculate finite-time survival probabilities in a structural model for credit risk, and thus obtain a closed-form pricing formula for a single-name credit default swap (CDS). This pricing formula is well calibrated on market CDS quotes. In particular, it explains why the par CDS credit spread is not negligible when the maturity becomes short.

KW - Credit default swap

KW - Finite-time survival probability

KW - First-passage time

KW - Lévy process

KW - Structural model

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U2 - 10.1016/j.insmatheco.2013.04.003

DO - 10.1016/j.insmatheco.2013.04.003

M3 - Article

AN - SCOPUS:84877677397

SN - 0167-6687

VL - 53

SP - 14

EP - 23

JO - Insurance: Mathematics and Economics

JF - Insurance: Mathematics and Economics

IS - 1

ER -

Finite-time survival probability and credit default swaps pricing under geometric Lévy markets

Abstract

Keywords

ASJC Scopus subject areas

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