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Pricing credit default swaps under a multi-scale stochastic volatility model

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  • Chen, Wenting
  • He, Xinjiang

Abstract

In this paper, we consider the pricing of credit default swaps (CDSs) with the reference asset driven by a geometric Brownian motion with a multi-scale stochastic volatility (SV), which is a two-factor volatility process with one factor controlling the fast time scale and the other representing the slow time scale. A key feature of the current methodology is to establish an equivalence relationship between the CDS and the down-and-out binary option through the discussion of “no default” probability, while balancing the two SV processes with the perturbation method. An approximate but closed-form pricing formula for the CDS contract is finally obtained, whose accuracy is in the order of O(ϵ+δ+ϵδ).

Suggested Citation

  • Chen, Wenting & He, Xinjiang, 2017. "Pricing credit default swaps under a multi-scale stochastic volatility model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 425-433.
    • Handle: RePEc:eee:phsmap:v:468:y:2017:i:c:p:425-433
    DOI: 10.1016/j.physa.2016.10.082
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    References listed on IDEAS

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    1. Duffie, Darrell & Singleton, Kenneth J, 1997. "An Econometric Model of the Term Structure of Interest-Rate Swap Yields," Journal of Finance, American Finance Association, vol. 52(4), pages 1287-1321, September.
    2. Robert A. Jarrow & Stuart M. Turnbull, 2008. "Pricing Derivatives on Financial Securities Subject to Credit Risk," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 17, pages 377-409, World Scientific Publishing Co. Pte. Ltd..
    3. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-470, May.
    4. Damiano Brigo & Kyriakos Chourdakis, 2009. "Counterparty Risk For Credit Default Swaps: Impact Of Spread Volatility And Default Correlation," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(07), pages 1007-1026.
    5. He, Xinjiang & Chen, Wenting, 2014. "The pricing of credit default swaps under a generalized mixed fractional Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 404(C), pages 26-33.
    6. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    7. repec:bla:jfinan:v:53:y:1998:i:6:p:2059-2106 is not listed on IDEAS
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    Cited by:

    1. Deng, Guohe, 2020. "Pricing perpetual American floating strike lookback option under multiscale stochastic volatility model," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).

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