Abstract
The Black-Scholes model and many of its extensions imply a log-normal distribution of stock returns. However, for holding periods of up to a year, the empirical return distribution (both conditional and unconditional) is not log-normal, but rather much closer to the logistic distribution. This paper derives analytic option pricing formulas for the case of the logistic return distribution. These formulas turn out to be simple and elegant, and employ exactly the same parameters as B&S. Moreover, empirically, the logistic option pricing formulas fit prices much better than B&S, and are comparable to much more sophisticated models with many more parameters.
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