The Inverted Parabola World of Classical Quantitative Finance: Non-Equilibrium and Non-Perturbative Finance Perspective

Abstract

Classical quantitative finance models such as the Geometric Brownian Motion or its later extensions such as local or stochastic volatility models do not make sense when seen from a physics-based perspective, as they are all equivalent to a negative mass oscillator with a noise. This paper presents an alternative formulation based on insights from physics.

Keywords: Geometric Brownian Motion, stochastic volatility, classical quantitative finance, physics, Langevin equations, negative mass oscillator, instantons

JEL Classification: G10, G11, G12, G13, C00, C02, C32, C50, C51, C52, C58, C60, C62, C65, C68, B23