Accurate modeling of the temporal evolution of asset prices is crucial for understanding financial markets. We explore the potential of discrete-time quantum walks to model the evolution of asset prices. Return distributions obtained from a model based on the quantum walk algorithm are compared with those obtained from classical methodologies. We focus on specific limitations of the classical models, and illustrate that the quantum walk model possesses great flexibility in overcoming these. This includes the potential to generate asymmetric return distributions with complex market tendencies and higher probabilities for extreme events than in some of the classical models. Furthermore, the temporal evolution in the quantum walk possesses the potential to provide asset price dynamics.
Accurate modeling of the temporal evolution of asset prices is crucial for understanding financial markets. We explore the potential of discrete-time quantum walks to model the evolution of asset prices. Return distributions obtained from a model based on the quantum walk algorithm are compared with those obtained from classical methodologies. We focus on specific limitations of the classical models, and illustrate that the quantum walk model possesses great flexibility in overcoming these. This includes the potential to generate asymmetric return distributions with complex market tendencies and higher probabilities for extreme events than in some of the classical models. Furthermore, the temporal evolution in the quantum walk possesses the potential to provide asset price dynamics.
We start with the idea that open quantum systems can be used to represent financial markets by modelling events from the external environment and their impact on the market price. We show how to characterize distinct orbits of the time evolution, and look at the development of the reduced density matrix, that represents the state of the market, over long time frames. In particular we distinguish between classical and non-classical modes of time evolution. We show that whilst both tend to the same set of maximum entropy states, this occurs faster in classical systems, with a knock on effect on the resulting probability distributions. We demonstrate how non-classical modes of time-evolution can be used to incorporate factors such as illiquid trades and imperfect trading mechanisms, and distinguish between different mechanisms of non-classical time evolution.
We start with the idea that open quantum systems can be used to represent financial markets by modelling events from the external environment and their impact on the market price. We show how to characterize distinct orbits of the time evolution, and look at the development of the reduced density matrix, that represents the state of the market, over long time frames. In particular we distinguish between classical and non-classical modes of time evolution. We show that whilst both tend to the same set of maximum entropy states, this occurs faster in classical systems, with a knock on effect on the resulting probability distributions. We demonstrate how non-classical modes of time-evolution can be used to incorporate factors such as illiquid trades and imperfect trading mechanisms, and distinguish between different mechanisms of non-classical time evolution.
We apply methods of quantum mechanics for mathematical modeling of price dynamics at the financial market. We propose to describe behavioral financial factors (e.g., expectations of traders) by using the pilot wave (Bohmian) model of quantum mechanics. Trajectories of prices are determined by two financial potentials: classical-like V ( q ) ("hard" market conditions, e.g., natural resources) and quantum-like U ( q ) (behavioral market conditions). On the one hand, our Bohmian model is a quantum-like model for the financial market, cf. with works of W. Segal, I. E. Segal, E. Haven, E. W. Piotrowski, J. Sladkowski. On the other hand, (since Bohmian mechanics provides the possibility to describe individual price trajectories) it belongs to the domain of extended research on deterministic dynamics for financial assets (C.W.J. Granger, W.A. Barnett, A. J. Benhabib, W.A. Brock, C. Sayers, J. Y. Campbell, A. W. Lo, A. C. MacKinlay, A. Serletis, S. Kuchta, M. Frank, R. Gencay, T. Stengos, M. J. Hinich, D. Patterson, D. A. Hsieh, D. T. Caplan, J.A. Scheinkman, B. LeBaron and many others).
Quantum computers have the potential to provide an advantage for financial pricing problems by the use of quantum estimation. In a broader context, it is reasonable to ask about situations where the market and the assets traded on the market themselves have quantum properties. In this work, we consider a financial setting where instead of by classical probabilities the market is described by a pure quantum state or, more generally, a quantum density operator. This setting naturally leads to a new asset class, which we call quantum assets. Under the assumption that such assets have a price and can be traded, we develop an extended definition of arbitrage to quantify gains without the corresponding risk. Our main result is a quantum version of the first fundamental theorem of asset pricing. If and only if there is no arbitrage, there exists a risk-free density operator under which all assets are martingales. This density operator is used for the pricing of quantum derivatives. To prove the theorem, we study the density operator version of the Radon-Nikodym measure change. We provide examples to illustrate the theory.
This review explores the emerging field of quantum-classical hybrid approaches for predicting stock price movement. Predicting the stock price movement has been a popular topic amongst machine learning (ML) enthusiasts. However, predicting how a particular stock or stock market will perform is a difficult task, due to market dynamics, company (stock) specific dynamics, volatility, and other environmental factors. Using advanced classic machine learning techniques, such predictions have become possible, but also computationally complex. There is a need to develop a non-linear prediction model for predicting the movement of the price of a stock, in a more accurate and faster manner. We examine recent advancements in quantum computing algorithms, focusing on the potential to enhance the efficiency and accuracy of traditional prediction models. This review delves into key concepts such as quantum feature maps, variational quantum circuits, and hybrid architectures that integrate quantum and classical components. We discuss the potential advantages of quantum-enhanced techniques, for their ability to process complex financial data efficiently and unlock hidden patterns. Furthermore, we analyze the current challenges and limitations. This review aims to provide an in-depth overview of the latest quantum-classical stock price prediction, highlighting promising avenues for further research and development in this exciting field.
This review explores the emerging field of quantum-classical hybrid approaches for predicting stock price movement. Predicting the stock price movement has been a popular topic amongst machine learning (ML) enthusiasts. However, predicting how a particular stock or stock market will perform is a difficult task, due to market dynamics, company (stock) specific dynamics, volatility, and other environmental factors. Using advanced classic machine learning techniques, such predictions have become possible, but also computationally complex. There is a need to develop a non-linear prediction model for predicting the movement of the price of a stock, in a more accurate and faster manner. We examine recent advancements in quantum computing algorithms, focusing on the potential to enhance the efficiency and accuracy of traditional prediction models. This review delves into key concepts such as quantum feature maps, variational quantum circuits, and hybrid architectures that integrate quantum and classical components. We discuss the potential advantages of quantum-enhanced techniques, for their ability to process complex financial data efficiently and unlock hidden patterns. Furthermore, we analyze the current challenges and limitations. This review aims to provide an in-depth overview of the latest quantum-classical stock price prediction, highlighting promising avenues for further research and development in this exciting field.