McCulloch, J. Huston. <br/><br/>
The Pricing of Short-Lived Options When Price Uncertainty Is Log-Symmetric Stable / 
J. Huston McCulloch. 
 - Cambridge, Mass.  National Bureau of Economic Research  1978. 
 - 1 online resource:  illustrations (black and white); 
 - NBER working paper series  no. w0264 .
 - Working Paper Series (National Bureau of Economic Research)  no. w0264. .
<br/><br/> July 1978. 
<br/><br/> 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. 
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