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American Step-up and Step-down Credit Default Swaps Under LÚvy Models

by Tim S.T. Leung of the Johns Hopkins University, and
Kazutoshi Yamazaki of the Osaka University

December 25, 2010

Abstract: This paper studies the valuation of a class of credit default swaps (CDSs) 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 CDS position. The pricing problem is formulated under a structural credit risk model based on LÚvy 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 LÚvy 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.

JEL Classification: G13, G33, D81, C61.

AMS Classification: 60G51, 91B25, 91B70.

Keywords: optimal stopping, credit default swaps, step-up and step-down options, LÚvy processes, scale functions

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