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@techreport{NBERw0264,
title = "The Pricing of Short-Lived Options When Price Uncertainty Is Log-Symmetric Stable",
author = "McCulloch, J. Huston",
institution = "National Bureau of Economic Research",
type = "Working Paper",
series = "Working Paper Series",
number = "264",
year = "1978",
month = "July",
doi = {10.3386/w0264},
URL = "http://www.nber.org/papers/w0264",
abstract = {The well-known option pricing formula of Black and Scholes depends upon the assumption that price fluctuations are log-normal. However, this formula greatly underestimates the value of options with a low probability of being exercised if, as appears to be more nearly the case in most markets, price fluctuations are in fact symmetrics table or log-symmetric stable. This paper derives a general formula for the value of a put or call option in a general equilibrium, expected utility maximization context. This general formula is found to yield the Black-Scholes formula for a wide variety of underlying processes generating log-normal price uncertainty. It is then used to derive the value of a short-lived option for certain processes that generate log-symmetric stable price uncertainty. Our analysis is restricted to short-lived options for reasons of mathematical tractability. Nevertheless, the formula is useful for evaluating many types of risk.},
}