An approximation formula for the price of credit default swaps under the fast-mean reversion volatility model

Xin-Jiang He; Wenting Chen

Applications of Mathematics (2019)

  • Volume: 64, Issue: 3, page 367-382
  • ISSN: 0862-7940

Abstract

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We consider the pricing of credit default swaps (CDSs) with the reference asset assumed to follow a geometric Brownian motion with a fast mean-reverting stochastic volatility, which is often observed in the financial market. To establish the pricing mechanics of the CDS, we set up a default model, under which the fair price of the CDS containing the unknown “no default” probability is derived first. It is shown that the “no default” probability is equivalent to the price of a down-and-out binary option written on the same reference asset. Based on the perturbation approach, we obtain an approximated but closed-form pricing formula for the spread of the CDS. It is also shown that the accuracy of our solution is in the order of 𝒪 ( ϵ ) .

How to cite

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He, Xin-Jiang, and Chen, Wenting. "An approximation formula for the price of credit default swaps under the fast-mean reversion volatility model." Applications of Mathematics 64.3 (2019): 367-382. <http://eudml.org/doc/294529>.

@article{He2019,
abstract = {We consider the pricing of credit default swaps (CDSs) with the reference asset assumed to follow a geometric Brownian motion with a fast mean-reverting stochastic volatility, which is often observed in the financial market. To establish the pricing mechanics of the CDS, we set up a default model, under which the fair price of the CDS containing the unknown “no default” probability is derived first. It is shown that the “no default” probability is equivalent to the price of a down-and-out binary option written on the same reference asset. Based on the perturbation approach, we obtain an approximated but closed-form pricing formula for the spread of the CDS. It is also shown that the accuracy of our solution is in the order of $\mathcal \{O\}(\epsilon )$.},
author = {He, Xin-Jiang, Chen, Wenting},
journal = {Applications of Mathematics},
keywords = {credit default swaps; fast mean-reverting volatility; perturbation method},
language = {eng},
number = {3},
pages = {367-382},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {An approximation formula for the price of credit default swaps under the fast-mean reversion volatility model},
url = {http://eudml.org/doc/294529},
volume = {64},
year = {2019},
}

TY - JOUR
AU - He, Xin-Jiang
AU - Chen, Wenting
TI - An approximation formula for the price of credit default swaps under the fast-mean reversion volatility model
JO - Applications of Mathematics
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 64
IS - 3
SP - 367
EP - 382
AB - We consider the pricing of credit default swaps (CDSs) with the reference asset assumed to follow a geometric Brownian motion with a fast mean-reverting stochastic volatility, which is often observed in the financial market. To establish the pricing mechanics of the CDS, we set up a default model, under which the fair price of the CDS containing the unknown “no default” probability is derived first. It is shown that the “no default” probability is equivalent to the price of a down-and-out binary option written on the same reference asset. Based on the perturbation approach, we obtain an approximated but closed-form pricing formula for the spread of the CDS. It is also shown that the accuracy of our solution is in the order of $\mathcal {O}(\epsilon )$.
LA - eng
KW - credit default swaps; fast mean-reverting volatility; perturbation method
UR - http://eudml.org/doc/294529
ER -

References

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