Closed Quantum Black-Scholes: Quantum Drift and the Heisenberg Equation of Motion

@article{Hicks2020ClosedQB,
  title={Closed Quantum Black-Scholes: Quantum Drift and the Heisenberg Equation of Motion},
  author={William Hicks},
  journal={Risk Management eJournal},
  year={2020}
}
  • William Hicks
  • Published 26 November 2019
  • Physics
  • Risk Management eJournal
In this article we model a financial derivative price as an observable on the market state function. We apply geometric techniques to integrating the Heisenberg Equation of Motion. We illustrate how the non-commutative nature of the model introduces quantum interference effects that can act as either a drag or a boost on the resulting return. The ultimate objective is to investigate the nature of quantum drift in the Accardi-Boukas quantum Black-Scholes framework which involves modelling the… 
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5 Citations
Background Citations
3
Methods Citations
1

5 Citations

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𝒫𝒯 Symmetry, Non-Gaussian Path Integrals, and the Quantum Black–Scholes Equation

TLDR
It is shown how certain nonlocal diffusions can be written as quantum stochastic processes, and how one can use path integral formalism, and PT symmetric quantum mechanics, to build a non-Gaussian kernel function for the Accardi–Boukas quantum Black–Scholes.

Nonlocal Diffusions and the Quantum Black-Scholes Equation: Modelling the Market Fear Factor

  • William Hicks
  • Mathematics
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  • 2018
In this paper, we establish a link between quantum stochastic processes, and nonlocal diffusions. We demonstrate how the non-commutative Black-Scholes equation of Accardi & Boukas (Luigi Accardi,…

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Motivated by the work of Segal and Segal on the Black-Scholes pricing formula in the quantum context, we study a quantum extension of the Black-Scholes equation within the context of…

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We analyze the properties of optimum portfolios, the price of which is considered a new quantum variable and derive a quantum analog of the Black-Scholes formula for the price of financial variables…

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