Quantum Mechanics, Path Integrals and Option Pricing: Reducing the Complexity of Finance

TL;DR

This paper explores how quantum mechanics and path integral methods can simplify complex option pricing models in finance, including lattice simulations and applications to nonlinear and exotic options.

Contribution

It introduces quantum-inspired path integral techniques to reduce computational complexity in option pricing, extending methods to nonlinear and path-dependent models.

Findings

Path integral methods effectively price simple options like Black-Scholes.

Quantum lattice simulations match analytical results for basic models.

Potential for applying these techniques to complex, exotic options.

Abstract

Quantum Finance represents the synthesis of the techniques of quantum theory (quantum mechanics and quantum field theory) to theoretical and applied finance. After a brief overview of the connection between these fields, we illustrate some of the methods of lattice simulations of path integrals for the pricing of options. The ideas are sketched out for simple models, such as the Black-Scholes model, where analytical and numerical results are compared. Application of the method to nonlinear systems is also briefly overviewed. More general models, for exotic or path-dependent options are discussed.