Related papers: Quantum diffusion of prices and profits
Quantum theory is used to model secondary financial markets. Contrary to stochastic descriptions, the formalism emphasizes the importance of trading in determining the value of a security. All possible realizations of investors holding…
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…
The present paper describes a practical example in which the probability distribution of the prices of a stock market blue chip is calculated as the wave function of a quantum particle confined in a potential well. This model may naturally…
The financial market is nonpredictable, as according to the Bachelier, the mathematical expectation of the speculator is zero. Nevertheless, we observe in the price fluctuations the two distinct scales, short and long time. Behaviour of a…
Large variations in stock prices happen with sufficient frequency to raise doubts about existing models, which all fail to account for non-Gaussian statistics. We construct simple models of a stock market, and argue that the large…
We present the general solutions for the classical and quantum dynamics of the anharmonic oscillator coupled to a purely diffusive environment. In both cases, these solutions are obtained by the application of the Baker-Campbell-Hausdorff…
We consider the problem of Bayesian inference for bi-variate data observed in time but with observation times which occur non-synchronously. In particular, this occurs in a wide variety of applications in finance, such as high-frequency…
One of the greatest contributors of the 20th century among all academician in the field of statistical finance, M. F. M. Osborne published in 1956 [6] an essential paper and proposed to treat the question of stock market motion through the…
Using Trades and Quotes data from the Paris stock market, we show that the random walk nature of traded prices results from a very delicate interplay between two opposite tendencies: long-range correlated market orders that lead to…
In this article we look at stochastic processes with uncertain parameters, and consider different ways in which information is obtained when carrying out observations. For example we focus on the case of a the random evolution of a traded…
The trade of a fixed stock can be regarded as the basic process that measures its momentary price. The stock price is exactly known only at the time of sale when the stock is between traders, that is, only in the case when the owner is…
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…
We explore nature of price formation in financial markets and develop a theory of bid and ask price dynamics in which the two prices form due to quantum-chaotic interaction between buy and sell orders. In this model bid and ask prices are…
The price of financial assets are, since Bachelier, considered to be described by a (discrete or continuous) time sequence of random variables, i.e a stochastic process. Sharp scaling exponents or unifractal behavior of such processes has…
Applications of Quantum Tunneling effect have long gone beyond the traditional physical meaning. Initially created by Gamow to explain {\alpha}-decay of nuclear particles, along the time, quantum tunneling found fertile domain of research…
We develop a theory of securities price formation and dynamics based on quantum approach and without presuming any similarities with quantum mechanics. Disorder introduced by trading environment leads to probability distribution of returns…
We use standard physics techniques to model trading and price formation in a market under the assumption that order arrival and cancellations are Poisson random processes. This model makes testable predictions for the most basic properties…
Stock price change in financial market occurs through transactions in analogy with diffusion in stochastic physical systems. The analysis of price changes in real markets shows that long-range correlations of price fluctuations largely…
In this paper, we consider a stochastic asset price model where the trend is an unobservable Ornstein Uhlenbeck process. We first review some classical results from Kalman filtering. Expectedly, the choice of the parameters is crucial to…
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…