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American step-up and step-down default swaps under Lévy 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 Lévy 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 Lévy 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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File URL: http://hdl.handle.net/10.1080/14697688.2012.730624
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Bibliographic Info

Article provided by Taylor & Francis Journals in its journal Quantitative Finance.

Volume (Year): 13 (2013)
Issue (Month): 1 (January)
Pages: 137-157

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Handle: RePEc:taf:quantf:v:13:y:2013:i:1:p:137-157

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  1. Tim Leung & Ronnie Sircar, 2009. "Accounting For Risk Aversion, Vesting, Job Termination Risk And Multiple Exercises In Valuation Of Employee Stock Options," Mathematical Finance, Wiley Blackwell, vol. 19(1), pages 99-128.
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Cited by:
  1. Masahiko Egami & Tim S. T. Leung & Kazutoshi Yamazaki, 2011. "Default Swap Games Driven by Spectrally Negative Levy Processes," Papers 1105.0238, arXiv.org, revised Sep 2012.

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