Early exercise boundary for American type of floating strike Asian option and its numerical approximation
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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- Asbjørn T. Hansen & Peter Løchte Jørgensen, 2000. "Analytical Valuation of American-Style Asian Options," Management Science, INFORMS, vol. 46(8), pages 1116-1136, August.
- 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.
- 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.
- 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.
- Andrea, Pascucci, 2007.
"Free boundary and optimal stopping problems for American Asian options,"
4766, University Library of Munich, Germany.
- Andrea Pascucci, 2008. "Free boundary and optimal stopping problems for American Asian options," Finance and Stochastics, Springer, vol. 12(1), pages 21-41, January.
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