The Analytical Valuation of American Average Rate Options

This article explores the analytic valuation of American average rate option based on the continuous arithmetic average in the Black-Scholes framework. Because there is no closed-form exact valuation formula for the average rate option with the arithmetic average, a very well-approximated arithmetic average density function is used for the valuation. The optimal exercise boundary and the values of American average rate options are compared with those of American plain vanilla options. Especially, this article shows that American average rate option can have two different optimal exercise boundaries depending on the current stock price. Numerical experiments are also performed to demonstrate the influence of the component factors on the values of American average rate options and to illustrate the accuracy and efficiency of the valuation formula.

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