Analytical Approximations for the Critical Stock Prices of American Options: A Performance Comparison
Posted: 15 Mar 2010
Date Written: March 11, 2010
Many efficient and accurate analytical methods for pricing American options now exist. However, while they can produce accurate option prices, they often do not give accurate critical stock prices. In this paper, we propose two new analytical approximations for American options based on the quadratic approximation. We compare our methods with existing analytical methods including the quadratic approximations in Barone-Adesi and Whaley (J Finance 42:301-320, 1987) and Barone-Adesi and Elliott (Stoch Anal Appl 9(2):115-131, 1991), the lower bound approximation in Broadie and Detemple (Rev Financial Stud 9:1211-1250, 1996), the tangent approximation in Bunch and Johnson (J Finance 55(5):2333-2356, 2000), the Laplace inversion method in Zhu (Int J Theor Appl Finance 9(7):1141-1177, 2006b), and the interpolation method in Li (Working paper, 2008). Both of our methods give much more accurate critical stock prices than all the existing methods above.
Keywords: American option, Analytical approximation, Critical stock price
JEL Classification: C02, C63, G13
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