Exercise boundary of the American put near maturity in an exponential Lévy model

Damien Lamberton () and Mohammed Mikou

Finance and Stochastics, 2013, vol. 17, issue 2, 355-394

Abstract: We study the behavior of the critical price of an American put option near maturity in an exponential Lévy model. In particular, we prove that in situations where the limit of the critical price is equal to the strike price, the rate of convergence to the limit is linear if and only if the underlying Lévy process has finite variation. In the case of infinite variation, a variety of rates of convergence can be observed: we prove that when the negative part of the Lévy measure exhibits an α-stable density near the origin, with 1>α>2, the convergence rate is ruled by $\theta^{1/\alpha}|\ln \theta|^{1-\frac{1}{\alpha}}$ , where θ is the time until maturity. Copyright Springer-Verlag 2013

Keywords: American put; Free boundary; Optimal stopping; Variational inequality; 60G40; 60G51; 91G20; G10; G12; G13 (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (4)

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Working Paper: Exercise Boundary of the American Put Near Maturity in an Exponential L\'evy Model (2011)
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DOI: 10.1007/s00780-012-0194-z

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