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American Step-Up and Step-Down Default Swaps under Levy Models

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  • Tim Siu-Tang Leung
  • Kazutoshi Yamazaki

Abstract

This paper studies the valuation of a class of default swaps with the embedded option to switch to a different premium and notional principal anytime prior to a credit event. These are early exercisable contracts that give the protection buyer or seller the right to step-up, step-down, or cancel the swap position. The pricing problem is formulated under a structural credit risk model based on Levy processes. This leads to the analytic and numerical studies of several optimal stopping problems subject to early termination due to default. In a general spectrally negative Levy model, we rigorously derive the optimal exercise strategy. This allows for instant computation of the credit spread under various specifications. Numerical examples are provided to examine the impacts of default risk and contractual features on the credit spread and exercise strategy.

Suggested Citation

  • Tim Siu-Tang Leung & Kazutoshi Yamazaki, 2010. "American Step-Up and Step-Down Default Swaps under Levy Models," Papers 1012.3234, arXiv.org, revised Sep 2012.
    • Handle: RePEc:arx:papers:1012.3234
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    References listed on IDEAS

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    Cited by:

    1. Egami, Masahiko & Leung, Tim & Yamazaki, Kazutoshi, 2013. "Default swap games driven by spectrally negative Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 123(2), pages 347-384.
    2. Zbigniew Palmowski & Budhi Surya, 2019. "Optimal valuation of American callable credit default swaps under drawdown of L\'evy insurance risk process," Papers 1904.10063, arXiv.org, revised Apr 2020.

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