Records 
Author 
Contreras, M.; Echeverria, J.; Pena, J.P.; Villena, M. 
Title 
Resonance phenomena in option pricing with arbitrage 
Type 

Year 
2020 
Publication 
Physica AStatistical Mechanics And Its Applications 
Abbreviated Journal 
Physica A 
Volume 
540 
Issue 

Pages 
21 pp 
Keywords 
BlackScholes 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 BlackScholes model. In Contreras et al. (2010), the authors after analyse empirical financial data, determines that the mispricing between the empirical and the BlackScholes 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 BlackScholes model. After that, in Contreras et al. (2010), the BlackScholes equation is generalised to incorporates explicitly these arbitrage bubbles, which generates an interaction potential that changes the usual BlackScholes free dynamics completely. However, an interesting phenomena appears when the amplitude of the arbitrage bubble is equal to the volatility parameter of the BlackScholes 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 
03784371 
ISBN 

Medium 

Area 

Expedition 

Conference 

Notes 
WOS:000506711900078 
Approved 

Call Number 
UAI @ eduardo.moreno @ 
Serial 
1095 
Permanent link to this record 



Author 
Contreras, M.; Montalva, R.; Pellicer, R.; Villena, M. 
Title 
Dynamic option pricing with endogenous stochastic arbitrage 
Type 

Year 
2010 
Publication 
Physica AStatistical Mechanics And Its Applications 
Abbreviated Journal 
Physica A 
Volume 
389 
Issue 
17 
Pages 
35523564 
Keywords 
BlackScholes model; Arbitrage; Option pricing 
Abstract 
Only few efforts have been made in order to relax one of the key assumptions of the BlackScholes model: the noarbitrage assumption. This is despite the fact that arbitrage processes usually exist in the real world, even though they tend to be shortlived. 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 tstep 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 BS 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 
03784371 
ISBN 

Medium 

Area 

Expedition 

Conference 

Notes 
WOS:000280118100023 
Approved 

Call Number 
UAI @ eduardo.moreno @ 
Serial 
91 
Permanent link to this record 



Author 
Contreras, M.; Pellicer, R.; Villena, M.; Ruiz, A. 
Title 
A quantum model of option pricing: When BlackScholes meets Schrodinger and its semiclassical limit 
Type 

Year 
2010 
Publication 
Physica AStatistical Mechanics And Its Applications 
Abbreviated Journal 
Physica A 
Volume 
389 
Issue 
23 
Pages 
54475459 
Keywords 
BlackScholes model; Arbitrage; Option pricing; Quantum mechanics; Semiclassical methods 
Abstract 
The BlackScholes 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, shortterm volatility, extreme discontinuities, or serial correlations; the classical nonarbitrage assumption of the BlackScholes model is violated, implying a nonriskfree portfolio. From Haven (2002) [1] we know that an arbitrage environment is a necessary condition to embedding the BlackScholes option pricing model in a more general quantum physics setting. The aim of this paper is to propose a new BlackScholesSchrodinger 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 BlackScholes 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 BlackScholes 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 
03784371 
ISBN 

Medium 

Area 

Expedition 

Conference 

Notes 
WOS:000283904000012 
Approved 

Call Number 
UAI @ eduardo.moreno @ 
Serial 
116 
Permanent link to this record 



Author 
Allende, H.; Elias, C.; Torres, S. 
Title 
Estimation of the option prime: Microsimulation of backward stochastic differential equations 
Type 

Year 
2004 
Publication 
International Statistical Review 
Abbreviated Journal 
Int. Stat. Rev. 
Volume 
72 
Issue 
1 
Pages 
107121 
Keywords 
BlackScholes 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 
03067734 
ISBN 

Medium 

Area 

Expedition 

Conference 

Notes 
WOS:000222159200009 
Approved 

Call Number 
UAI @ eduardo.moreno @ 
Serial 
45 
Permanent link to this record 