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On the Perpetual American Put Options for Level Dependent Volatility Models with Jumps

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  • Erhan Bayraktar

Abstract

We prove that the perpetual American put option price of level dependent volatility model with compound Poisson jumps is convex and is the classical solution of its associated quasi-variational inequality, that it is $C^2$ except at the stopping boundary and that it is $C^1$ everywhere (i.e. the smooth pasting condition always holds).

Suggested Citation

  • Erhan Bayraktar, 2007. "On the Perpetual American Put Options for Level Dependent Volatility Models with Jumps," Papers math/0703538, arXiv.org, revised Jan 2009.
    • Handle: RePEc:arx:papers:math/0703538
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    References listed on IDEAS

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    1. Carr, Peter, 1998. "Randomization and the American Put," The Review of Financial Studies, Society for Financial Studies, vol. 11(3), pages 597-626.
    2. L. Alili & A. E. Kyprianou, 2005. "Some remarks on first passage of Levy processes, the American put and pasting principles," Papers math/0508487, arXiv.org.
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