Abstract
In this paper, a simple algorithm to improve the computational accuracy of the analytical approximation for the value of American put options and their optimal exercise boundary proposed by Zhu (Int. J. Theor. Appl. Finance 9(7):1141–1177, 2006) is presented. In the current approach, Zhu’s simple approximation formula is used as an initial guess for the optimal exercise boundary of American put options. The determination of an improved optimal exercise boundary is then achieved by setting a null value of the Theta of option on the optimal exercise boundary. Numerical test results show that the improvement in accuracy is indeed significant in determining the optimal exercise boundary.
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Zhu, SP. A simple approximation formula for calculating the optimal exercise boundary of American puts. J. Appl. Math. Comput. 37, 611–623 (2011). https://doi.org/10.1007/s12190-010-0454-z
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DOI: https://doi.org/10.1007/s12190-010-0454-z