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

@article{Hicks2018NonlocalDA, title={Nonlocal Diffusions and the Quantum Black-Scholes Equation: Modelling the Market Fear Factor}, author={William Hicks}, journal={Risk Management \& Analysis in Financial Institutions eJournal}, year={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, Andreas Boukas, 'The Quantum Black-Scholes Equation', Jun 2007, available at arXiv:0706.1300v1) can be written in integral form. This enables the application of the Monte-Carlo methods adapted to McKean stochastic differential equations (H. P. McKean, 'A class of Markov processes associated with…

## 5 Citations

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

- PhysicsEntropy
- 2019

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.

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

- PhysicsEntropy
- 2019

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.

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

- PhysicsJournal of Stochastic Analysis
- 2020

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…

### Pseudo-Hermiticity and Removing Brownian Motion From Finance

- Mathematics
- 2020

In this article we apply the methods of quantum mechanics to the study of the financial markets. Specifically, we discuss the Pseudo-Hermiticity of the Hamiltonian operators associated to the typical…

### A Nonlocal Approach to The Quantum Kolmogorov Backward Equation and Links to Noncommutative Geometry

- PhysicsCommunications on Stochastic Analysis
- 2019

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…

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