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Author Contreras, M.; Echeverria, J.; Pena, J.P.; Villena, M. doi  openurl
  Title Resonance phenomena in option pricing with arbitrage Type
  Year (down) 2020 Publication Physica A-Statistical Mechanics And Its Applications Abbreviated Journal Physica A  
  Volume 540 Issue Pages 21 pp  
  Keywords Black-Scholes model; Option pricing; Arbitrage; Barrier options  
  Abstract In this paper, we want to report an interesting resonance phenomena that appears in option pricing, when the presence of arbitrage is incorporated explicitly into the Black-Scholes model. In Contreras et al. (2010), the authors after analyse empirical financial data, determines that the mispricing between the empirical and the Black-Scholes prices can be described by Heaviside type function (called an arbitrage bubble there). These bubbles are characterised by a finite time span and an amplitude which measures the price deviation from the Black-Scholes model. After that, in Contreras et al. (2010), the Black-Scholes equation is generalised to incorporates explicitly these arbitrage bubbles, which generates an interaction potential that changes the usual Black-Scholes free dynamics completely. However, an interesting phenomena appears when the amplitude of the arbitrage bubble is equal to the volatility parameter of the Black-Scholes model: in that case, the potential becomes infinite, and option pricing decrease abruptly to zero. We analyse this limit behaviour for two situations: a European and a barrier option. Also, we perform an analytic study of the propagator in each case, to understand the cause of the resonance. We think that it resonance phenomena could to help to understand the origin of certain financial crisis in the option pricing area. (C) 2019 Elsevier B.V. All rights reserved.  
  Address [Contreras, M.; Pena, J. P.] Univ Andres Bello, Dept Ciencias Fis, Sazie 2212, Chile, Email: mauriccio1965@gmail.com;  
  Corporate Author Thesis  
  Publisher Elsevier 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:000506711900078 Approved  
  Call Number UAI @ eduardo.moreno @ Serial 1095  
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Author Contreras, M.; Montalva, R.; Pellicer, R.; Villena, M. pdf  doi
openurl 
  Title Dynamic option pricing with endogenous stochastic arbitrage Type
  Year (down) 2010 Publication Physica A-Statistical Mechanics And Its Applications Abbreviated Journal Physica A  
  Volume 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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Author Contreras, M.; Pellicer, R.; Villena, M.; Ruiz, A. pdf  doi
openurl 
  Title A quantum model of option pricing: When Black-Scholes meets Schrodinger and its semi-classical limit Type
  Year (down) 2010 Publication Physica A-Statistical Mechanics And Its Applications Abbreviated Journal Physica A  
  Volume 389 Issue 23 Pages 5447-5459  
  Keywords Black-Scholes model; Arbitrage; Option pricing; Quantum mechanics; Semi-classical methods  
  Abstract The Black-Scholes equation can be interpreted from the point of view of quantum mechanics, as the imaginary time Schrodinger equation of a free particle. When deviations of this state of equilibrium are considered, as a product of some market imperfection, such as: Transaction cost, asymmetric information issues, short-term volatility, extreme discontinuities, or serial correlations; the classical non-arbitrage assumption of the Black-Scholes model is violated, implying a non-risk-free portfolio. From Haven (2002) [1] we know that an arbitrage environment is a necessary condition to embedding the Black-Scholes option pricing model in a more general quantum physics setting. The aim of this paper is to propose a new Black-Scholes-Schrodinger model based on the endogenous arbitrage option pricing formulation introduced by Contreras et al. (2010) [2]. Hence, we derive a more general quantum model of option pricing, that incorporates arbitrage as an external time dependent force, which has an associated potential related to the random dynamic of the underlying asset price. This new resultant model can be interpreted as a Schrodinger equation in imaginary time for a particle of mass 1/sigma(2) with a wave function in an external field force generated by the arbitrage potential. As pointed out above, this new model can be seen as a more general formulation, where the perfect market equilibrium state postulated by the Black-Scholes model represent a particular case. Finally, since the Schrodinger equation is in place, we can apply semiclassical methods, of common use in theoretical physics, to find an approximate analytical solution of the Black-Scholes equation in the presence of market imperfections, as it is the case of an arbitrage bubble. Here, as a numerical illustration of the potential of this Schrodinger equation analogy, the semiclassical approximation is performed for different arbitrage bubble forms (step, linear and parabolic) and compare with the exact solution of our general quantum model of option pricing. (C) 2010 Elsevier B.V. All rights reserved.  
  Address [Contreras, Mauricio; Pellicer, Rely; Villena, Marcelo; Ruiz, Aaron] Adolfo Ibanez Univ, Fac Sci & Engn, Santiago, 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:000283904000012 Approved  
  Call Number UAI @ eduardo.moreno @ Serial 116  
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Author Allende, H.; Elias, C.; Torres, S. pdf  url
openurl 
  Title Estimation of the option prime: Microsimulation of backward stochastic differential equations Type
  Year (down) 2004 Publication International Statistical Review Abbreviated Journal Int. Stat. Rev.  
  Volume 72 Issue 1 Pages 107-121  
  Keywords Black-Scholes model; stochastic differential equations; options prime; hedging strategy  
  Abstract A mathematical statistical model is needed to obtain an option prime and create a hedging strategy. With formulas derived from stochastic differential equations, the primes for US Dollar/Chilean Pesos currency options using a prime calculator are obtained. Furthermore, a backward simulation of the option prime trajectory is used with a numerical method created for backward stochastic differential equations. The use of statistics in finance is highly important in order to develop complex products.  
  Address Univ Tecn Federico Santa Maria, Dept Informat, Valparaiso, Chile  
  Corporate Author Thesis  
  Publisher Int Statistical Inst Place of Publication Editor  
  Language English Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0306-7734 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000222159200009 Approved  
  Call Number UAI @ eduardo.moreno @ Serial 45  
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