Approximation of American put prices by European prices via an embedding method.
type: Item
instance of: scholarly article
title: Approximation of American put prices by European prices via an embedding method.
zbMATH Open document ID: 1033.60051
author: Benjamin Jourdain
author: Claude Martini
published in: The Annals of Applied Probability
publication date: 2003-05-06T00:00:00Z
review text: American options differ from their European counterparts since the exercise date is at the holder's disposal and not fixed in advance. This feature makes American options more valuable and more difficult to price since no closed-form solutions are available and one has to rely on approximate solutions obtained by solving numerically a free boundary problem. The authors apply the theoretical result of the authors [Ann. Inst. Henri Poincaré, Anal. Non Linéaire 18, No. 1, 1--17 (2001; Zbl 0982.60028)] to propose a numerical scheme to price an American put option in the Black-Scholes model. The method, named amusingly YAAAP (Yet Another Approximation for the American Put), fares quite well when compared with a finite-difference method, and the LUBA and Ju methods. The main contribution of the scheme is the procedure itself. According to the theoretical result mentioned above, the American price of certain payoffs coincides with the European price of an associated claim. But, even for an American put with strike \(K\), the corresponding European payoff is unknown. Nevertheless, the authors define a parametrized family of claims that match the payoff of the American put at least outside \((k^*,k)\), where \(k^*\) is the perpetual strike, for which the European price can be computed. Finally, they propose a procedure to choose the ``best'' member of that family to approximate the American put value and delta. Therefore this approach also provides an approximate hedging strategy and could be used to price other options.
reviewed by: Miguel Ángel Mirás Calvo
Mathematics Subject Classification ID: 60G40
Mathematics Subject Classification ID: 60G46
Mathematics Subject Classification ID: 91B28
zbMATH DE Number: 1906195
zbMATH Keywords: option pricing
zbMATH Keywords: American options
zbMATH Keywords: free boundary problems
zbMATH Keywords: approximation methods
zbMATH Keywords: optimal stopping
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aoap/1015961161
OpenAlex ID: W1966215153
cites work: Q5285464
cites work: Multigrid Algorithms for the Solution of Linear Complementarity Problems Arising from Free Boundary Problems
cites work: ALTERNATIVE CHARACTERIZATIONS OF AMERICAN PUT OPTIONS
cites work: American prices embedded in European prices
cites work: Q4848526
DOI: 10.1214/AOAP/1015961161
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description: scientific article; zbMATH DE number 1906195