02039cam a22002777 4500001000600000003000500006005001700011006001900028007001500047008004100062100002600103245011000129260006600239300005700305490004100362500001500403520095900418530006001377538007201437538003601509588002501545710004201570830007601612856003701688856003601725w0264NBER20200704151414.0m o d cr cnu||||||||200704s1978 mau fo 000 0 eng d1 aMcCulloch, J. Huston.14aThe Pricing of Short-Lived Options When Price Uncertainty Is Log-Symmetric Stable /cJ. Huston McCulloch. aCambridge, Mass.bNational Bureau of Economic Researchc1978. a1 online resource:billustrations (black and white);1 aNBER working paper seriesvno. w0264 aJuly 1978.3 aThe 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. aHardcopy version available to institutional subscribers aSystem requirements: Adobe [Acrobat] Reader required for PDF files. aMode of access: World Wide Web.0 aPrint version record2 aNational Bureau of Economic Research. 0aWorking Paper Series (National Bureau of Economic Research)vno. w0264.40uhttp://www.nber.org/papers/w026440uhttp://dx.doi.org/10.3386/w0264