The Pricing of Short-Lived Options When Price Uncertainty Is Log-Symmetric Stable / J. Huston McCulloch.

Format:

Book

Author/Creator:

McCulloch, J. Huston.

Contributor:

National Bureau of Economic Research.

Series:

Working Paper Series (National Bureau of Economic Research) no. w0264.

NBER working paper series no. w0264

Language:

English

Subjects (All):

Economic history.

Physical Description:

1 online resource: illustrations (black and white);

Place of Publication:

Cambridge, Mass. National Bureau of Economic Research 1978.

Cambridge, Mass. : National Bureau of Economic Research, 1978.

Summary:

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.

Notes:

Print version record

July 1978.