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A Put Option Paradox

Published online by Cambridge University Press:  06 April 2009

Mark Grinblatt  and
Herb Johnson
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Abstract

What happens to the price of a put in a period during which the stock price stays constant? The hedging strategy implicit in the Black-Scholes model would seem to imply that the put goes up in value. Pure arbitrage arguments imply the opposite result. This paper resolves the paradox and uses it to explore the restrictions inherent in the diffusion processes assumed for all option pricing models.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 23 , Issue 1 , March 1988 , pp. 23 - 26
Copyright
Copyright © School of Business Administration, University of Washington 1988

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References

Black, F., and Scholes, M.. “The Pricing of Options and Corporate Liabilities.” Journal of Political Economy, 81 (05/06 1973), 637–659.Google Scholar
Cox, J.; Ross, S.; and Rubinstein, M.. “Option Pricing: A Simplified Approach.” Journal of Financial Economics, 7 (09 1979), 229–263.CrossRefGoogle Scholar
Cox, J., and Rubinstein, M.. Options Markets. Englewood Cliffs, NJ: Prentice Hall (1985).Google Scholar