Quantum finance market analysis with wave functions.

Is Quantum Finance the Next Big Thing? A Beginner's Guide to Modeling Asset Returns

Lena Kashyap in Business & Economy December 2025 • 4 min read.

"Discover how quantum probability is revolutionizing asset return modeling and what it means for your investment strategy."

The financial markets are complex systems driven by countless interactions between investors. These interactions, influenced by differing beliefs, strategies, and information access, result in inevitable price fluctuations. Traditionally, these fluctuations and their impact on asset returns have been analyzed using stochastic process models, which rely on probabilistic laws to capture market randomness.

A new approach is emerging, one that leverages quantum theory and its unique mathematical framework. Known as quantum finance, this field applies quantum probability to model asset returns. Unlike traditional methods, quantum finance offers a fresh perspective by using complex numbers to represent probabilities, opening doors to capturing nuances previously unseen.

This article explores the core concepts of quantum finance, highlighting its potential to revolutionize asset return modeling. We will delve into how quantum probability works, its relationship to classical probability, and how it can be applied to understand market behavior and improve investment strategies.

Quantum Probability: Beyond Classical Models

Quantum finance market analysis with wave functions.

Classical probability models have long been the standard for understanding asset returns. However, these models often fall short in capturing the full complexity of market dynamics. Quantum probability offers an alternative by extending classical probability from real numbers to complex numbers. This extension introduces a 'phase' component, which allows for the modeling of phenomena that classical models struggle to represent, such as potential periodicities and local multimodal distributions.

In essence, quantum probability provides a more comprehensive mathematical scheme for describing the statistical behavior of asset returns. The key difference lies in the ability to represent probabilities as complex numbers, offering a richer framework for capturing market nuances.

Modulus: After squaring, the modulus corresponds directly to the probability size, similar to classical probability.
Phase: This additional component captures the potential periodicity of probability changes and helps model the local multimodal nature of asset return distributions.

This additional element makes quantum probability advantageous in characterizing multimodal distributions of asset returns. The fluctuating prices in financial markets cause assets to form distributions of holding costs at various price levels. This can lead to multi-modal characteristics, making quantum probability a suitable tool for modeling asset return behavior.

The Schrödinger-Like Trading Equation: Bridging Theory and Practice

By applying Fourier decomposition, a Schrödinger-like trading equation can be derived. Although it formally resembles the Schrödinger equation in quantum theory, it originates entirely from non-microscopic trading behavior. The variables involved, such as kinetic and potential energy terms and energy levels, have corresponding financial interpretations. This equation implies discrete energy levels in financial trading, where returns follow a normal distribution at the lowest level. As the market advances to higher trading levels, a phase transition occurs in the return distribution, leading to multimodality and fat tails. This framework is supported by empirical research conducted on the Chinese stock market.

About this Article -

This article was crafted using a human-AI hybrid and collaborative approach. AI assisted our team with initial drafting, research insights, identifying key questions, and image generation. Our human editors guided topic selection, defined the angle, structured the content, ensured factual accuracy and relevance, refined the tone, and conducted thorough editing to deliver helpful, high-quality information.See our About page for more information.

This article is based on research published under:

DOI-LINK: https://doi.org/10.48550/arXiv.2401.05823,

Title: Quantum Probability Theoretic Asset Return Modeling: A Novel Schr\"Odinger-Like Trading Equation And Multimodal Distribution

Subject: q-fin.mf

Authors: Li Lin

Published: 11-01-2024

Everything You Need To Know

What is Quantum Finance, and how does it differ from traditional finance?

Quantum Finance is a novel approach that applies quantum probability to model asset returns. Unlike traditional methods that use classical probability with real numbers, Quantum Finance extends it to complex numbers. This allows for the incorporation of a 'phase' component, which helps capture nuances in the market that classical models often miss. Specifically, it enables modeling of phenomena like potential periodicities and local multimodal distributions in asset returns. It is the use of quantum theory and its unique mathematical framework to analyze and understand financial markets.

How does quantum probability enhance the understanding of asset return modeling compared to classical probability?

Quantum probability provides a more comprehensive mathematical scheme by representing probabilities as complex numbers. This introduces a 'phase' component in addition to the modulus. The modulus, after squaring, corresponds to probability size, similar to classical probability. However, the phase component captures potential periodicities and models the local multimodal nature of asset return distributions. This is particularly advantageous in characterizing the complex distributions of holding costs at various price levels, allowing for a more nuanced understanding of market behavior.

Can you explain the significance of the Schrödinger-like trading equation in Quantum Finance?

The Schrödinger-like trading equation is derived by applying Fourier decomposition. While it resembles the Schrödinger equation from quantum theory, it originates from non-microscopic trading behavior. It introduces financial interpretations for variables like kinetic and potential energy, which reflect trading dynamics. This equation suggests discrete energy levels in financial trading. At the lowest level, returns follow a normal distribution. As trading levels increase, a phase transition occurs, leading to multimodality and fat tails in the return distribution, reflecting more complex market dynamics.

What are the key components of quantum probability and how do they contribute to asset return modeling?

The key components are the modulus and the phase. The modulus, when squared, represents the probability size, similar to classical probability models. The phase is the additional component in quantum probability, which captures the potential periodicity of probability changes. It helps model the local multimodal nature of asset return distributions. This is particularly useful in finance because fluctuating prices in financial markets cause assets to form distributions of holding costs at various price levels, often resulting in multi-modal characteristics.

How can Quantum Finance improve investment strategies, and what are its potential advantages?

Quantum Finance potentially improves investment strategies by offering a more nuanced understanding of market behavior. By using quantum probability, it can capture phenomena that are difficult to model with classical methods, such as potential periodicities and multimodal distributions. This leads to the development of models like the Schrödinger-like trading equation, which can provide insights into market dynamics, allowing investors to better predict market trends. This framework can be used to improve investment strategies, providing better insights into market dynamics, including helping model more accurate risk assessments.