A Quantum-like Approach to the Stock Market

TL;DR

This paper explores a quantum-like framework for stock market behavior, emphasizing the contextual and nonclassical nature of stock prices, especially during crises, and introduces a sphere model to support quantum modeling in finance.

Contribution

It applies the SCoP formalism and a sphere model to demonstrate the nonclassical, contextual behavior of stock prices, providing a theoretical basis for quantum models in finance.

Findings

Stock prices are context-dependent and not definite until traded.

Quantum-like models can describe market behavior during crises.

The sphere model illustrates non-Kolmogorovian probability structures in finance.

Abstract

Modern approaches to stock pricing in quantitative finance are typically founded on the 'Black-Scholes model' and the underlying 'random walk hypothesis'. Empirical data indicate that this hypothesis works well in stable situations but, in abrupt transitions such as during an economical crisis, the random walk model fails and alternative descriptions are needed. For this reason, several proposals have been recently forwarded which are based on the formalism of quantum mechanics. In this paper we apply the 'SCoP formalism', elaborated to provide an operational foundation of quantum mechanics, to the stock market. We argue that a stock market is an intrinsically contextual system where agents' decisions globally influence the market system and stocks prices, determining a nonclassical behavior. More specifically, we maintain that a given stock does not generally have a definite value, e.g., a price, but its value is actualized as a consequence of the contextual interactions in the trading process. This contextual influence is responsible of the non-Kolmogorovian quantum-like behavior of the market at a statistical level. Then, we propose a 'sphere model' within our 'hidden measurement formalism' that describes a buying/selling process of a stock and shows that it is intuitively reasonable to assume that the stock has not a definite price until it is traded. This result is relevant in our opinion since it provides a theoretical support to the use of quantum models in finance.