The Pricing of Short-Lived Options When Price Uncertainty Is Log-Symmetric Stable

J. Huston McCulloch

No 264, NBER Working Papers from National Bureau of Economic Research, Inc

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.

Date: 1978-07
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Published as McCulloch, J. Huston. "The Value of European Options and Log-Stable Uncertainty," International Advances in Economic Research. Volume 3, Number 4 / November, 1997

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