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An Analytic Approximation for the American Put Price

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  • Johnson, H. E.

Abstract

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.

Suggested Citation

  • Johnson, H. E., 1983. "An Analytic Approximation for the American Put Price," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 18(1), pages 141-148, March.
    • Handle: RePEc:cup:jfinqa:v:18:y:1983:i:01:p:141-148_01
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