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Pricing American options for jump diffusions by iterating optimal stopping problems for diffusions

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Abstract

We approximate the price of the American put for jump diffusions by a sequence of functions, which are computed iteratively. This sequence converges to the price function uniformly and exponentially fast. Each element of the approximating sequence solves an optimal stopping problem for geometric Brownian motion, and can be numerically computed using the classical finite difference methods. We prove the convergence of this numerical scheme and present examples to illustrate its performance.

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Authors and Affiliations

  1. Department of Mathematics, University of Michigan, Ann Arbor, MI, 48109, USA

    Erhan Bayraktar & Hao Xing

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  1. Erhan Bayraktar
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  2. Hao Xing
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Correspondence to Erhan Bayraktar.

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This research is supported in part by the National Science Foundation.

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Bayraktar, E., Xing, H. Pricing American options for jump diffusions by iterating optimal stopping problems for diffusions. Math Meth Oper Res 70, 505–525 (2009). https://doi.org/10.1007/s00186-008-0282-1

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  • DOI: https://doi.org/10.1007/s00186-008-0282-1

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