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Author Contreras, M.; Montalva, R.; Pellicer, R.; Villena, M.
Title Dynamic option pricing with endogenous stochastic arbitrage Type
Year 2010 Publication Physica A-Statistical Mechanics And Its Applications Abbreviated Journal Physica A
Volume (down) 389 Issue 17 Pages 3552-3564
Keywords Black-Scholes model; Arbitrage; Option pricing
Abstract Only few efforts have been made in order to relax one of the key assumptions of the Black-Scholes model: the no-arbitrage assumption. This is despite the fact that arbitrage processes usually exist in the real world, even though they tend to be short-lived. The purpose of this paper is to develop an option pricing model with endogenous stochastic arbitrage, capable of modelling in a general fashion any future and underlying asset that deviate itself from its market equilibrium. Thus, this investigation calibrates empirically the arbitrage on the futures on the S&P 500 index using transaction data from September 1997 to June 2009, from here a specific type of arbitrage called “arbitrage bubble”, based on a t-step function, is identified and hence used in our model. The theoretical results obtained for Binary and European call options, for this kind of arbitrage, show that an investment strategy that takes advantage of the identified arbitrage possibility can be defined, whenever it is possible to anticipate in relative terms the amplitude and timespan of the process. Finally, the new trajectory of the stock price is analytically estimated for a specific case of arbitrage and some numerical illustrations are developed. We find that the consequences of a finite and small endogenous arbitrage not only change the trajectory of the asset price during the period when it started, but also after the arbitrage bubble has already gone. In this context, our model will allow us to calibrate the B-S model to that new trajectory even when the arbitrage already started. (C) 2010 Elsevier B.V. All rights reserved.
Address [Contreras, Mauricio; Montalva, Rodrigo; Pellicer, Rely; Villena, Marcelo] Univ Adolfo Ibanez, Fac Sci & Engn, Vina Del Mar, Chile, Email: mauricio.contreras@uai.cl
Corporate Author Thesis
Publisher Elsevier Science Bv Place of Publication Editor
Language English Summary Language Original Title
Series Editor Series Title Abbreviated Series Title
Series Volume Series Issue Edition
ISSN 0378-4371 ISBN Medium
Area Expedition Conference
Notes WOS:000280118100023 Approved
Call Number UAI @ eduardo.moreno @ Serial 91
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