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A discussion on embedding the Black-Scholes option pricing model in a quantum physics setting
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In this article, the authors consider embedding the Black-Scholes option pricing model within a quantum physical setting and show that the advantages of doing so may indeed provide for a first step to include arbitrage in a natural way in an otherwise arbitrage free model.Abstract:
In this paper we consider the implications of embedding the Black–Scholes option pricing model within a quantum physical setting. The option price is considered to be a state function and a potential function is found which allows the option price to satisfy the Schrodinger differential equation. Once this arbitrage-free potential function is obtained, we argue for the construction of a so-called ‘arbitrage’ potential function. This functional is instrumental in determining the existence of a ‘financial’ state function. We show the existence of an arbitrage-free price when the potential function converges to one. The existence of arbitrage hinges on the non-zero value of the Planck constant. This constant is then linked to a parameter which regulates the probability of occurence of strategy paths. We call this parameter the ‘belief’ parameter. We argue that it is the belief parameter which may indeed proxy arbitrage. The outcome of this paper shows that the Black–Scholes model can be captured within a quantum physical setting and that the advantages of doing so may indeed provide for a first step to include arbitrage in a natural way in an otherwise arbitrage free model.read more
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References
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Quantum Mechanics and Path Integrals
TL;DR: Au sommaire as discussed by the authors developed the concepts of quantum mechanics with special examples and developed the perturbation method in quantum mechanics and the variational method for probability problems in quantum physics.
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Advanced mathematical methods for scientists and engineers
Carl M. Bender,Steven A. Orszag +1 more
TL;DR: A self-contained presentation of the methods of asymptotics and perturbation theory, methods useful for obtaining approximate analytical solutions to differential and difference equations is given in this paper.
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Physics of Finance: Gauge Modelling in Non-Equilibrium Pricing
TL;DR: Fibre Bundles in finance: First Contact Fibre bundles in finance as discussed by the authors : Fibre bundles in mathematics: First contact, first contact, and the first contact.
Journal ArticleDOI
Exact solution of a modified El Farol's bar problem: Efficiency and the role of market impact
TL;DR: In this paper, a model of heterogeneous, inductive rational agents inspired by the El Farol Bar problem and the Minority Game is discussed, where agents follow a simple reinforcement learning dynamics where the reinforcement, for each of their available strategies, is related to the payoff delivered by that strategy.
Journal ArticleDOI
A path integral approach to option pricing with stochastic volatility : Some exact results
TL;DR: The Black-Scholes formula for pricing options on stocks and other securities has been generalized by Merton and Garman to the case when stock volatility is stochastic.