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American step-up and step-down default swaps under L�vy models

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  • Tim 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 L�vy 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 L�vy 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.

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  • Tim Leung & Kazutoshi Yamazaki, 2013. "American step-up and step-down default swaps under L�vy models," Quantitative Finance, Taylor & Francis Journals, vol. 13(1), pages 137-157, January.
    • Handle: RePEc:taf:quantf:v:13:y:2013:i:1:p:137-157
    DOI: 10.1080/14697688.2012.730624
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    Citations

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    Cited by:

    1. Hongzhong Zhang, 2018. "Stochastic Drawdowns," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 10078, December.
    2. Jiao Li, 2016. "Trading VIX Futures under Mean Reversion with Regime Switching," Papers 1605.07945, arXiv.org, revised Jun 2016.
    3. Mitya Boyarchenko & Sergei Levendorskiĭ, 2015. "Ghost calibration and the pricing of barrier options and CDS in spectrally one-sided L�vy models: the parabolic Laplace inversion method," Quantitative Finance, Taylor & Francis Journals, vol. 15(3), pages 421-441, March.
    4. Tim Leung & Kazutoshi Yamazaki & Hongzhong Zhang, 2015. "An Analytic Recursive Method For Optimal Multiple Stopping: Canadization And Phase-Type Fitting," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(05), pages 1-31.
    5. Jiao Li, 2016. "Trading VIX futures under mean reversion with regime switching," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(03), pages 1-20, September.
    6. Kazutoshi Yamazaki, 2017. "Inventory Control for Spectrally Positive Lévy Demand Processes," Mathematics of Operations Research, INFORMS, vol. 42(1), pages 212-237, January.
    7. Kazutoshi Yamazaki, 2016. "Optimality of two-parameter strategies in stochastic control," Papers 1605.04995, arXiv.org.
    8. Tim Leung & Hongzhong Zhang, 2017. "Optimal Trading with a Trailing Stop," Papers 1701.03960, arXiv.org, revised Mar 2019.
    9. Hernández-Hernández, Daniel & Yamazaki, Kazutoshi, 2015. "Games of singular control and stopping driven by spectrally one-sided Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 125(1), pages 1-38.

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