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An Analytic Approximation for the American Put Price

Published online by Cambridge University Press:  06 April 2009

H. E. Johnson
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Extract

Black and Scholes [1] derived the pricing equation for a European put when the stock price follows geometric Brownian motion. For this same case, Merton [5] derived the pricing equation for an American put with infinite time to maturity. Brennan and Schwartz [2], Rubinstein and Cox [7], and Parkinson [6] have developed numerical solutions for the price of an American put. Numerical solutions are expensive and do not provide much intuition. Naturally, an analytic solution would be much preferred; unfortunately, pricing the American put requires solving a formidable and presumably intractable boundary value problem.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 18 , Issue 1 , March 1983 , pp. 141 - 148
Copyright
Copyright © School of Business Administration, University of Washington 1983

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References

[1]Black, F., and Scholes, M.. “The Pricing of Options and Corporate Liabilities.” Journal of Political Economy, Vol. 81 (05/06 1973), pp. 637–659.CrossRefGoogle Scholar
[2]Brennan, M., and Schwartz, E.. “The Valuation of American Put Options.” Journal of Finance, Vol. 32 (05 1977), pp. 449–462.CrossRefGoogle Scholar
[3]Dahlquist, G., and Bjorck, A.. Numerical Methods. Englewood Cliffs, NJ: Prentice-Hall (1974).Google Scholar
[4]Margrabe, W. “The Value of an Option to Exchange One Asset for Another.” Journal of Finance, Vol. 33 (03 1978), pp. 177–186.CrossRefGoogle Scholar
[5]Merton, R. “The Theory of Rational Option Pricing.” Bell Journal of Economics and Management Science, Vol. 4 (Spring 1973), pp. 141–183.Google Scholar
[6]Parkinson, M. “Option Pricing: the American Put.” Journal of Business Vol. 50 (01 1977), pp. 21–36.CrossRefGoogle Scholar
[7]Rubinstein, M., and Cox, J.. Options Markets. Englewood Cliffs, NJ: Prentice-Hall (1982).Google Scholar