An Analytic Approximation for the American Put Price for Options on Stocks with Dividends

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Abstract
In a recent paper, Johnson [7] has given an analytic approximation to the American put price that delivers values that are very close to numerical solutions. The limitation to the Johnson approximation is that it is only applicable to put options on stocks without cash dividends. This study modifies the Johnson approximation to value options on stocks that have one exdividend date prior to the option expiration date, and these approximation values are compared to the analytic solutions provided by the Geske and Johnson [6] American put option pricing model. The approximation values are generally very close to the analytic solutions.

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