Unlike European-type derivative securities, there are no simple analytic valuation formulas for finite-lived American options, even when the underlying asset price has constant volatility. The early exercise feature considerably complicates the valuation of American contracts. The strategy taken in this paper is to rely on nonparametric statistical methods using market data to estimate the call prices and the exercise boundaries. A comparison is made with parametric constant volatility model-based prices and exercise boundaries. The paper focuses on assessing the adequacy of conventional formulas by comparing them to nonparametric estimates. We use daily market option prices and exercise data on the S&P100 contract, the most actively traded American option contract. We find large discrepancies between the parametric and nonparametric call prices and exercise boundaries. We also find remarkable similarities of the nonparametric estimates before and after the crash of October 1987.
Broadie, Mark, Jerome Detemple, Eric Ghysels, and O. Torres. "Nonparametric Estimation of American Option Exercise Boundaries and Call Prices." Journal of Economic Dynamics and Control 24, no. 11-12 (2000): 1829-57.
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