TY - JOUR
AU - McCulloch, J. Huston
TI - The Pricing of Short-Lived Options When Price Uncertainty Is Log-Symmetric Stable
JF - National Bureau of Economic Research Working Paper Series
VL - No. 264
PY - 1978
Y2 - July 1978
DO - 10.3386/w0264
UR - http://www.nber.org/papers/w0264
L1 - http://www.nber.org/papers/w0264.pdf
N1 - Author contact info:
J. Huston McCulloch
AB - 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.
ER -