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

TL;DR

This paper models financial derivatives using quantum mechanics, applying geometric techniques to the Heisenberg Equation of Motion, revealing quantum interference effects that influence market dynamics in a novel quantum Black-Scholes framework.

Contribution

It introduces a quantum approach to financial modeling by integrating the Heisenberg Equation of Motion, highlighting quantum interference effects in derivative pricing.

Findings

Quantum interference can act as a drag or boost on returns.

The model differentiates between external noise and fundamental quantum randomness.

Application of geometric techniques to quantum financial models.

Abstract

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 financial market as a quantum observable, and introduces randomness through the Hudson-Parthasarathy quantum stochastic calculus. In particular we aim to differentiate randomness that is introduced through external noise (quantum stochastic calculus) and randomness that is fundamental to a quantum system (Heisenberg Equation of Motion).