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Yet Another Approximation of the American Put

Benjamin Jourdain 1 Claude Martini 1
1 MATHFI - Financial mathematics
Inria Paris-Rocquencourt, ENPC - École des Ponts ParisTech, UPEC UP12 - Université Paris-Est Créteil Val-de-Marne - Paris 12
Abstract : In this paper, as an application of the theoretical result in [1], we exhibit a family of payoffs $\widehat\varphi _h (x) indexed by a measure h, for the American price of which an almost closed formula holds, which are very close to the Put payoff in the following sense: they are continuous, match with (K-x)+ outside of the range ]K*,K[ (where K* is the perpetual Put strike), are analytic inside with the right derivative (-1) at both ends. Moreover a numerical procedure to select the best h in some sense yields excellent results. The first interest is to yield the corresponding sub- and super- very sharp hedging strategies, since there is a hedge ratio associated to our price. Also since the error is smoothed by the probability of crossing the free boundary, the corresponding errors regarding the price is much smaller, thus yielding good approximations of the Black-Scho- les American Put price.
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Submitted on : Wednesday, May 24, 2006 - 10:59:30 AM
Last modification on : Thursday, February 3, 2022 - 11:14:19 AM
Long-term archiving on: : Thursday, March 24, 2011 - 12:16:03 PM


  • HAL Id : inria-00072805, version 1



Benjamin Jourdain, Claude Martini. Yet Another Approximation of the American Put. [Research Report] RR-3851, INRIA. 2000. ⟨inria-00072805⟩



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