# The American Put Option Valued Analytically

The American Put Option Valued Analytically ABSTRACT An analytic solution to the American put problem is derived herein. The hedge ratio and other derivatives of the solution are presented. The formula derived implies an exact duplicating portfolio for the American put consisting of discount bonds and stock sold short. The formula is extended to consider put options on stocks paying cash dividends. A polynomial expression is developed for evaluating these formulae. Values and hedge ratios for puts on both dividend and nondividend paying stocks are calculated, tabulated, and compared with values derived by numerical integration and binomial approximation. As with European options, evaluating an analytic formula is more efficient than approximating the stock price process or the partial differential equation by binomial or finite difference methods. Finally, applications of this American put solution are discussed. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png The Journal of Finance Wiley

# The American Put Option Valued Analytically

The Journal of Finance, Volume 39 (5) – Dec 1, 1984
14 pages

/lp/wiley/the-american-put-option-valued-analytically-EsCjRCd4Dk
Publisher
Wiley
1984 The American Finance Association
ISSN
0022-1082
eISSN
1540-6261
DOI
10.1111/j.1540-6261.1984.tb04921.x
Publisher site
See Article on Publisher Site

### Abstract

ABSTRACT An analytic solution to the American put problem is derived herein. The hedge ratio and other derivatives of the solution are presented. The formula derived implies an exact duplicating portfolio for the American put consisting of discount bonds and stock sold short. The formula is extended to consider put options on stocks paying cash dividends. A polynomial expression is developed for evaluating these formulae. Values and hedge ratios for puts on both dividend and nondividend paying stocks are calculated, tabulated, and compared with values derived by numerical integration and binomial approximation. As with European options, evaluating an analytic formula is more efficient than approximating the stock price process or the partial differential equation by binomial or finite difference methods. Finally, applications of this American put solution are discussed.

### Journal

The Journal of FinanceWiley

Published: Dec 1, 1984

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