Dynamic option pricing with endogenous stochastic arbitrage

Contreras, Mauricio; Montalva, Rodrigo; Pellicer, Rely; Villena, Marcelo

doi:10.1016/j.physa.2010.04.019

Cited by 15 publications

(36 citation statements)

References 16 publications

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“…The existence results for di erent types of linear Schrödinger equations can be found in book [22]. Stock options pricing models based on linear Schrödinger equations and their relation to Black-Scholes models are reported in many papers [23][24][25][26][27][28][29]. Among others in the author's previous paper [29], the European call option price based on the linear Schrödinger equation has been calculated.…”

Section: U(t S(t)) = Max{ S(t) − K}mentioning

confidence: 99%

Nonlinear Schrödinger approach to European option pricing

Wróblewski

2017

Open Physics

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This paper deals with numerical option pricing methods based on a Schrödinger model rather than the Black-Scholes model. Nonlinear Schrödinger boundary value problems seem to be alternatives to linear models which better re ect the complexity and behavior of real markets. Therefore, based on the nonlinear Schrödinger option pricing model proposed in the literature, in this paper a model augmented by external atomic potentials is proposed and numerically tested. In terms of statistical physics the developed model describes the option in analogy to a pair of two identical quantum particles occupying the same state. The proposed model is used to price European call options on a stock index. the model is calibrated using the Levenberg-Marquardt algorithm based on market data. A Runge-Kutta method is used to solve the discretized boundary value problem numerically. Numerical results are provided and discussed. It seems that our proposal more accurately models phenomena observed in the real market than do linear models.

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Section: U(t S(t)) = Max{ S(t) − K}mentioning

confidence: 99%

Nonlinear Schrödinger approach to European option pricing

Wróblewski

2017

Open Physics

View full text Add to dashboard Cite

show abstract

“…[2] we proposed a generalization (called the CPV-model) of the Black-Scholes model including arbitrage possibilities, but in a endogenous way. For this CPV-model, the usual equation used in the arbitrage-free hypothesis is changed into…”

Section: The Basic Disequilibrium Financial Modelmentioning

confidence: 99%

“…Then the CPV-model developed in Ref. [2] corresponds, from a physics point of view, to an interacting particle with an external field force. It is important to mention that, as the BS one, this equation belongs to the Backward Kolmogorov PDE family.…”

Section: The Basic Disequilibrium Financial Modelmentioning

confidence: 99%

“…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-Schrödinger 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.…”

Section: Introductionmentioning

confidence: 99%

“…[2]. Thus, we will 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.…”

Section: Introductionmentioning

confidence: 99%

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