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

Bayraktar, Erhan and Xing, Hao (2009) Analysis of the optimal exercise boundary of American options for jump diffusions. SIAM Journal on Mathematical Analysis, 41 (2). pp. 825-860. ISSN 0036-1410

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## Abstract

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.

Item Type: Article http://epubs.siam.org/ © 2009 Society for Industrial and Applied Mathematics H Social Sciences > HA Statistics Departments > Statistics http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx 28 Jan 2011 15:41 http://eprints.lse.ac.uk/31868/