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Early exercise boundary for American type of floating strike Asian option and its numerical approximation

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  • Tomas Bokes
  • Daniel Sevcovic

Abstract

In this paper we generalize and analyze the model for pricing American-style Asian options due to (Hansen and Jorgensen 2000) by including a continuous dividend rate $q$ and a general method of averaging of the floating strike. We focus on the qualitative and quantitative analysis of the early exercise boundary. The first order Taylor series expansion of the early exercise boundary close to expiry is constructed. We furthermore propose an efficient numerical algorithm for determining the early exercise boundary position based on the front fixing method. Construction of the algorithm is based on a solution to a nonlocal parabolic partial differential equation for the transformed variable representing the synthesized portfolio. Various numerical results and comparisons of our numerical method and the method developed by (Dai and Kwok 2006) are presented.

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File URL: http://arxiv.org/pdf/0912.1321
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Paper provided by arXiv.org in its series Papers with number 0912.1321.

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Date of creation: Dec 2009
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Handle: RePEc:arx:papers:0912.1321

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Web page: http://arxiv.org/

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  1. Asbjørn T. Hansen & Peter Løchte Jørgensen, 2000. "Analytical Valuation of American-Style Asian Options," Management Science, INFORMS, vol. 46(8), pages 1116-1136, August.
  2. Andrea Pascucci, 2008. "Free boundary and optimal stopping problems for American Asian options," Finance and Stochastics, Springer, vol. 12(1), pages 21-41, January.
  3. Daniel Sevcovic, 2007. "An iterative algorithm for evaluating approximations to the optimal exercise boundary for a nonlinear Black-Scholes equation," Papers 0710.5301, arXiv.org.
  4. Rachel Kuske & Joseph Keller, 1998. "Optimal exercise boundary for an American put option," Applied Mathematical Finance, Taylor & Francis Journals, vol. 5(2), pages 107-116.
  5. Geske, Robert & Johnson, Herb E, 1984. " The American Put Option Valued Analytically," Journal of Finance, American Finance Association, vol. 39(5), pages 1511-24, December.
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Cited by:
  1. Daniel Sevcovic & Martin Takac, 2011. "Sensitivity analysis of the early exercise boundary for American style of Asian options," Papers 1101.3071, arXiv.org.
  2. Tomas Bokes, 2010. "A unified approach to determining the early exercise boundary position at expiry for American style of general class of derivatives," Papers 1012.0348, arXiv.org, revised Mar 2011.
  3. J. D. Kandilarov & D. Sevcovic, 2011. "Comparison of Two Numerical Methods for Computation of American Type of the Floating Strike Asian Option," Papers 1106.0020, arXiv.org.

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