Option Pricing beyond Black-Scholes Model:Quantum Mechanics Approach

TL;DR

This paper introduces a quantum mechanics-inspired model to extend the Black-Scholes option pricing framework, allowing for the incorporation of unexpected market behaviors and forces.

Contribution

It proposes a novel market force driven model based on quantum harmonic oscillator analogies, enabling more flexible and realistic option pricing schemes.

Findings

New option pricing schemes accounting for unexpected market forces

Identification of risk premiums linked to emergent market behaviors

Analysis of various market forces' effects on option prices

Abstract

Based on the analog between the stochastic dynamics and quantum harmonic oscillator, we propose a market force driving model to generalize the Black-Scholes model in finance market. We give new schemes of option pricing, in which we can take various unexpected market behaviors into account to modify the option pricing. As examples, we present several market forces to analyze their effects on the option pricing. These results provide us two practical applications. One is to be used as a new scheme of option pricing when we can predict some hidden market forces or behaviors emerging. The other implies the existence of some risk premium when some unexpected forces emerge.