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American-Style Options- The Effect of American-Style Options

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American-Style Options

The Effect of American-Style Options
The ability to exercise early has no effect on the price of calls in the absence of dividends and only a moderate impact if dividends are taken into account. The principal difference between European- and American-style options occurs for put premiums. For American-style options, there is a significant upward effect on put premiums, whether or not dividends are present. Unfortunately, there is no neat, concise, and exact formula for American-style put premiums. A good analytic approximation for these premiums is given by a formula developed by Giovanni Barone-Adesi and Robert Whaley, as follows:

where the European put premium is the one calculated using the Merton variation, and P* is the critical stock price determined from the procedure outlined below. The early exercise premium is given by:

where:

N(-h*) again denotes the cumulative normal distribution function, where h* is the dividend adjusted parameter specified in the Merto…