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

  title={Closed Quantum Black-Scholes: Quantum Drift and the Heisenberg Equation of Motion},
  author={William Hicks},
  journal={Risk Management eJournal},
  • 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… 
Wild Randomness and the Application of Hyperbolic Diffusion in Financial Modelling
The application of the Cauchy distribution has often been discussed as a potential model of the financial markets. In particular the way in which single extreme, or "Black Swan", events can impact


𝒫𝒯 Symmetry, Non-Gaussian Path Integrals, and the Quantum Black–Scholes Equation
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
    Communications on Stochastic Analysis
  • 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,
A Nonlocal Approach to the Quantum Kolmogorov Backward Equation and Links to Noncommutative Geometry
The Accardi-Boukas quantum Black-Scholes equation can be used as an alternative to the classical approach to finance, and has been found to have a number of useful benefits. The quantum Kolmogorov
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
Quantum-like approach to financial risk: quantum anthropic principle
We continue the analysis of quantum-like description of market phenomena and economics. We show that it is possible to define a risk inclination operator acting in some Hilbert space that has a lot
Quantum Analog of the Black- Scholes Formula(market of financial derivatives as a continuous weak measurement)
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
Quantum Theory for Mathematicians
1 The Experimental Origins of Quantum Mechanics.- 2 A First Approach to Classical Mechanics.- 3 A First Approach to Quantum Mechanics.- 4 The Free Schrodinger Equation.- 5 A Particle in a Square
Spectral Theorem Approach to the Characteristic Function of Quantum Observables
Using the spectral theorem we compute the Quantum Fourier Transform (or Vacuum Characteristic Function) $\langle \Phi, e^{itH}\Phi\rangle$ of an observable $H$ defined as a self-adjoint sum of the