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

By:

McCulloch, J. Huston

Contributor(s):

National Bureau of Economic Research

Material type: Text

TextSeries: Working Paper Series (National Bureau of Economic Research) ; no. w0264.Publication details: Cambridge, Mass. National Bureau of Economic Research 1978.Description: 1 online resource: illustrations (black and white)Online resources:

Available additional physical forms:

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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.

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Item type	Home library	Collection	Call number	Status	Date due	Barcode	Item holds
Working Paper	Biblioteca Digital	Colección NBER	nber w0264 (Browse shelf(Opens below))	Not For Loan

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July 1978.

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.