English

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

Mathematical Finance 2020-01-27 v3

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).

Keywords

Cite

@article{arxiv.1911.11475,
  title  = {Closed Quantum Black-Scholes: Quantum Drift and the Heisenberg Equation of Motion},
  author = {Will Hicks},
  journal= {arXiv preprint arXiv:1911.11475},
  year   = {2020}
}