Quantum effects in an expanded Black-Scholes model

TL;DR

This paper explores quantum-inspired modifications to the Black-Scholes model, incorporating non-commuting operators to better match actual market prices of European call options, suggesting quantum effects influence financial markets.

Contribution

It introduces a quantum-inspired expanded Black-Scholes model that accounts for non-commuting information processes, improving the accuracy of option pricing.

Findings

The expanded model better fits actual market prices.

Imaginary components in the model account for pricing disparities.

Quantum effects may influence financial market dynamics.

Abstract

The limitations of the classical Black-Scholes model are examined by comparing calculated and actual historical prices of European call options on stocks from several sectors of the S&P 500. Persistent differences between the two prices point to an expanded model proposed by Segal and Segal (1998) in which information not simultaneously observable or actionable with public information can be represented by an additional pseudo-Wiener process. A real linear combination of the original and added processes leads to a commutation relation analogous to that between a boson field and its canonical momentum in quantum field theory. The resulting pricing formula for a European call option replaces the classical volatility with the norm of a complex quantity, whose imaginary part is shown to compensate for the disparity between prices obtained from the classical Black-Scholes model and actual prices of the test call options. This provides market evidence for the influence of a non-classical process on the price of a security based on non-commuting operators.