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Analysis of the optimal exercise boundary of American options for jump diffusions

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In this paper we show that the optimal exercise boundary/free boundary of the American put option pricing problem for jump diffusions is continuously differentiable (except at maturity). This differentiability result was established by Yang, Jiang, and Bian [European J. Appl. Math., 17 (2006), pp. 95–127] in the case where the condition $r\geq q+\lambda\int_{\mathbb{R}_+}\,(e^z-1)\,\nu(dz)$ is satisfied. We extend the result to the case where the condition fails using a unified approach that treats both cases simultaneously. We also show that the boundary is infinitely differentiable under a regularity assumption on the jump distribution.

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en

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http://eprints.lse.ac.uk/31868/

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