The 1900 Option Formula: Why an At-the-Money Call Is Worth Two Fifths of a Swing
A share swinging twenty dollars a year gives an at-the-money call that looks like it should cost ten, half the swing collected half the time. It costs 7.98, because the upper half of a bell curve averages 0.798 of a standard deviation rather than a whole one. The article derives the general arithmetic-Brownian price, checks both limits, and quantifies the negative-price defect that got the model retired and then rehabilitated.