Optimal exercise of American options under stock pinning

dc.affiliation.dptoUC3M. Departamento de Estadísticaes
dc.contributor.authorD'Auria, Bernardo
dc.contributor.authorGarcía Portugués, Eduardo
dc.contributor.authorGuada-Azze, Abel
dc.contributor.editorUniversidad Carlos III de Madrid. Departamento de Estadísticaes
dc.contributor.funderEuropean Commissionen
dc.contributor.funderMinisterio de Economía y Competitividad (España)es
dc.description.abstractWe 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.en
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.en
dc.relation.ispartofseriesWorking paper. Statistics and Econometricsen
dc.relation.projectIDGobierno de España. MTM2017-85618-Pes
dc.relation.projectIDGobierno de España. MTM2015-72907-EXPes
dc.relation.projectIDGobierno de España. PGC2018-097284-B-I00es
dc.relation.projectIDGobierno de España. IJCI-2017-32005es
dc.relation.projectIDGobierno de España. MTM2016-76969-Pes
dc.rightsAtribución-NoComercial-SinDerivadas 3.0 España*
dc.rights.accessRightsopen accessen
dc.subject.otherAmerican Optionen
dc.subject.otherBrownian Bridgeen
dc.subject.otherFree-Boundary Problemen
dc.subject.otherOptimal Stoppingen
dc.subject.otherOption Pricingen
dc.subject.otherPut-Call Parityen
dc.subject.otherStock Pinningen
dc.titleOptimal exercise of American options under stock pinningen
dc.typeworking paper*
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
1.77 MB
Adobe Portable Document Format