Geodesic
An approximation formula for the price of credit default swaps under the fast-mean reversion volatility model
Applications of Mathematics, Tome 64 (2019) no. 3, pp. 367-382

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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 $\mathscr O(\epsilon )$.
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 $\mathscr O(\epsilon )$.
DOI : 10.21136/AM.2019.0313-17
Classification : 91G20, 91G80
Keywords: credit default swaps; fast mean-reverting volatility; perturbation method 
He, Xin-Jiang; Chen, Wenting. An approximation formula for the price of credit default swaps under the fast-mean reversion volatility model. Applications of Mathematics, Tome 64 (2019) no. 3, pp. 367-382. doi: 10.21136/AM.2019.0313-17
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     title = {An approximation formula for the price of credit default swaps under the fast-mean reversion volatility model},
     journal = {Applications of Mathematics},
     pages = {367--382},
     year = {2019},
     volume = {64},
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     language = {en},
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