Applications of Mathematics, Vol. 64, No. 3, pp. 367-382, 2019
An approximation formula for the price of credit default swaps under the fast-mean reversion volatility model
Xin-Jiang He, Wenting Chen
Received November 13, 2017. Published online April 9, 2019.
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 $\mathscr O(\epsilon)$.
Keywords: credit default swaps; fast mean-reverting volatility; perturbation method
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Affiliations: Xin-Jiang He, School of Mathematics and Applied Statistics, University of Wollongong, Northfields Ave, Wollongong NSW 2522, Australia; Wenting Chen (corresponding author), School of Business, Jiangnan University, Liangjiang Rd, Binhu Qu, Wuxi Shi, Jiangsu Sheng, China, e-mail: cwtwxuow@gmail.com
