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

Journal Article


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 O(ε).

Authors


Publication Date


  • 2019

Citation


  • He, X. & Chen, W. (2019). An approximation formula for the price of credit default swaps under the fast-mean reversion volatility model. Applications of Mathematics, 64 (3), 367-382.

Scopus Eid


  • 2-s2.0-85065403440

Number Of Pages


  • 15

Start Page


  • 367

End Page


  • 382

Volume


  • 64

Issue


  • 3

Place Of Publication


  • Czech Republic

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 O(ε).

Authors


Publication Date


  • 2019

Citation


  • He, X. & Chen, W. (2019). An approximation formula for the price of credit default swaps under the fast-mean reversion volatility model. Applications of Mathematics, 64 (3), 367-382.

Scopus Eid


  • 2-s2.0-85065403440

Number Of Pages


  • 15

Start Page


  • 367

End Page


  • 382

Volume


  • 64

Issue


  • 3

Place Of Publication


  • Czech Republic