Critical Stock Price Near Expiration

Barles, Guy; Burdeau, Julien; Romano, Marc; Samsoen, Nicolas

doi:10.1111/j.1467-9965.1995.tb00103.x

Cited by 114 publications

(67 citation statements)

References 12 publications

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“…This agrees with previous studies by Barles et al [4] and Kuske and Keller [6], who used different methods to consider the same problem.…”

Section: Discussionsupporting

confidence: 83%

“…Finally, we mention in passing that in this study, as was the case with those of Barles et al [4] and Kuske and Keller [6], we have assumed that the underlying stock prices follow a log-normal random walk, or geometric Brownian motion, and that the value of an option obeys the Black-Scholes equation. Ait-Sahalia (Ait-Sahalia [1] and Ait-Sahalia and Lo [2]) has considered the case where the price of the underlying stock obeys a more complex stochastic process; he showed that the price of an option could be found using state-price densities or SPD's, which can be estimated non-parametrically using market data, rather than relying on specific assumptions.…”

Section: Discussionmentioning

confidence: 99%

“…Barles et al [4] were able to find upper and lower bounds for the optimal exercise boundary near to expiration and then prove that these upper and lower bounds approached each other as expiration was approached, leading them to conclude that the value of the option behaved like…”

Section: Introductionmentioning

confidence: 99%

“…Kuske and Keller [6] derived an integral equation for the free boundary using a Green's function method and solved it iteratively. They stopped after three iterations, with the leading order term on their solution agreeing with that of Barles et al [4]. In what follows, we will attempt to use an asymptotic analysis to analyse the free boundary near to expiration, and see why a naïve expansion will not work, and what must be done to make an expansion work.…”

Section: Introductionmentioning

confidence: 99%

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On the optimal exercise boundary for an American put option

Alobaidi

Mallier

2001

Journal of Applied Mathematics

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An American put option is a derivative financial instrument that gives its holder the right but not the obligation to sell an underlying security at a pre-determined price. American options may be exercised at any time prior to expiry at the discretion of the holder, and the decision as to whether or not to exercise leads to a free boundary problem. In this paper, we examine the behavior of the free boundary close to expiry. Working directly with the underlying PDE, by using asymptotic expansions, we are able to deduce this behavior of the boundary in this limit.

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“…This agrees with previous studies by Barles et al [4] and Kuske and Keller [6], who used different methods to consider the same problem.…”

Section: Discussionsupporting

confidence: 83%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On the optimal exercise boundary for an American put option

Alobaidi

Mallier

2001

Journal of Applied Mathematics

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“…This is the intuition underlying this limiting result stated in Proposition 1.4.4. The American option exercise boundary is studied in detail in Ait-Sahlia 1995 and Barles, et al 1995 . See also van Moerbeke 1976 .…”

Section: Standard American Options: the Gbmp Modelmentioning

confidence: 99%

American options on dividend-paying assets

Broadie¹,

Detemple²

1998

Topology and Markets

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Montréal mars 1996Typeset by A M S-T E X Ce document est publié dans l'intention de rendre accessibles les résultats préliminaires de la recherche effectuée au CIRANO, afin de susciter des échanges et des suggestions. Les Les organisations-partenaires / The Partner Organizations•Ministère de l'Industrie, du Commerce, de la Science et de la Technologie.•École des Hautes Études Commerciales.•École Polytechnique.•Université de Montréal.•Université Laval.•McGill University.•Université du Québec à Montréal.•Bell Québec.•La Caisse de dépôt et de placement du Québec.•Hydro-Québec.•Fédération des caisses populaires de Montréal et de l'Ouest-du-Québec.•Téléglobe Canada.•Société d'électrolyse et de chimie Alcan Ltée.•Avenor.•Service de développement économique de la ville de Montréal.•Raymond, Chabot, Martin, Paré •Banque Nationale du Canada

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American Options

Chevalier

2010

Encyclopedia of Quantitative Finance

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We present the main results concerning the American options theory. We give the characterization of the American option value process as the Snell envelope of the option pay‐off process. Consequently, we describe optimal exercise times and derive a hedging strategy for the option. We also explain how this is used for numerical methods based on dynamic programming equation. In the second section of the article, we study the analytic approach to American option valuation. Option prices are solutions of variational inequalities and can be approximated using finite difference methods. Finally, we quote some properties of the exercise region. In particular, we give the early exercise premium formula that links the American and European options prices and allows to obtain an integral equation for exercise boundaries.

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Critical Stock Price Near Expiration

Cited by 114 publications

References 12 publications

On the optimal exercise boundary for an American put option

On the optimal exercise boundary for an American put option

American options on dividend-paying assets

American Options

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