Optimal exercise of American options under stock pinning

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dc.contributor.author D'Auria, Bernardo
dc.contributor.author García Portugués, Eduardo
dc.contributor.author Guada-Azze, Abel
dc.contributor.editor Universidad Carlos III de Madrid. Departamento de Estadística
dc.date.accessioned 2019-09-12T14:53:21Z
dc.date.available 2019-09-12T14:53:21Z
dc.date.issued 2019-09-11
dc.identifier.issn 2387-0303
dc.identifier.uri http://hdl.handle.net/10016/28803
dc.description.abstract We address the problem of optimally exercising American options based on the assumption that the underlying stock's price follows a Brownian bridge whose final value coincides with the strike price. In order to do so, we solve the discounted optimal stopping problem endowed with the gain function G(x) = (S-x)+ and a Brownian bridge whose final value equals S. These settings came up as a first approach of optimally exercising an option within the so-called "stock pinning" scenario. The optimal stopping boundary for this problem is proved to be the unique solution, up to certain regularity conditions, of an integral equation, which is then numerically solved by an algorithm hereby exposed. We face the case where the volatility is unspecified by providing an estimated optimal stopping boundary that, alongside with pointwise confidence intervals, provide alternative stopping rules. Finally, we demonstrate the usefulness of our method within the stock pinning scenario through a comparison with the optimal exercise time based on a geometric Brownian motion. We base our comparison on the contingent claims and the 5-minutes intraday stock price data of Apple and IBM for the period 2011-2018. Supplementary materials with the main proofs and auxiliary lemmas are available online.
dc.description.sponsorship [Bernardo D'Auria] Supported by projects MTM2017-85618-P and MTM2015-72907-EXP from the Spanish Ministry of Economy, Industry and Competitiveness, and the European Regional Development Fund. [Eduardo García-Portugués] Supported by projects PGC2018-097284-B-I00, IJCI-2017-32005, and MTM2016-76969-P from the Spanish Ministry of Economy, Industry and Competitiveness, and the European Regional Development Fund. [Abel Guada-Azze] Supported by a scholarship from the Department of Statistics of Universidad Carlos III de Madrid.
dc.language.iso eng
dc.relation.ispartofseries Working paper. Statistics and Econometrics
dc.relation.ispartofseries 19-13
dc.rights Atribución-NoComercial-SinDerivadas 3.0 España
dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subject.other American Option
dc.subject.other Brownian Bridge
dc.subject.other Free-Boundary Problem
dc.subject.other Optimal Stopping
dc.subject.other Option Pricing
dc.subject.other Put-Call Parity
dc.subject.other Stock Pinning
dc.title Optimal exercise of American options under stock pinning
dc.type workingPaper
dc.rights.accessRights openAccess
dc.relation.projectID Gobierno de España. MTM2017-85618-P
dc.relation.projectID Gobierno de España. MTM2015-72907-EXP
dc.relation.projectID Gobierno de España. PGC2018-097284-B-I00
dc.relation.projectID Gobierno de España. IJCI-2017-32005
dc.relation.projectID Gobierno de España. MTM2016-76969-P
dc.type.version draft
dc.identifier.uxxi DT/0000001725
dc.contributor.funder European Commission
dc.contributor.funder Ministerio de Economía y Competitividad (España)
dc.affiliation.dpto UC3M. Departamento de Estadística
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