On Valuing American Call Options with the Black‐Scholes European Formula

Abstract

Empirical papers on option pricing have uncovered systematic differences between market prices and values produced by the Black‐Scholes European formula. Such "biases" have been found related to the exercise price, the time to maturity, and the variance. We argue here that the American option variant of the Black‐Scholes formula has the potential to explain the first two biases and may partly explain the third. It can also be used to understand the empirical finding that the striking price bias reverses itself in different sample periods. The expected form of the striking price bias is explained in detail and is shown to be closely related to past empirical findings.

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