Related papers: A Quantum Approach to Stock Price Fluctuations
We present a finite-dimensional version of the quantum model for the stock market proposed in [C. Zhang and L. Huang, A quantum model for the stock market, Physica A 389(2010) 5769]. Our approach is an attempt to make this model consistent…
Quantum theory provides a comprehensive framework for quantifying uncertainty, often applied in quantum finance to explore the stochastic nature of asset returns. This perspective likens returns to microscopic particle motion, governed by…
Standard quantitative models of the stock market predict a log-normal distribution for stock returns (Bachelier 1900, Osborne 1959), but it is recognised (Fama 1965) that empirical data, in comparison with a Gaussian, exhibit leptokurtosis…
A new model for stock price fluctuations is proposed, based upon an analogy with the motion of tracers in Gaussian random fields, as used in turbulent dispersion models and in studies of transport in dynamically disordered media. Analytical…
Price fluctuations of commodities like cotton and wheat are thought to display probability distributions of returns that follow a L\'evy stable distribution. Recent analysis of stocks and foreign exchange markets show that the probability…
Financial time series typically exhibit strong fluctuations that cannot be described by a Gaussian distribution. In recent empirical studies of stock market indices it was examined whether the distribution P(r) of returns r(tau) after some…
We generalize the recently proposed quantum model for the stock market by Zhang and Huang to make it consistent with the discrete nature of the stock price. In this formalism, the price of the stock and its trend satisfy the generalized…
The quotient of random variables with normal distributions is examined and proven to have have power law decay, with density $f\left( x\right) \simeq f_{0}x^{-2}$, with the coefficient depending on the means and variances of the numerator…
With the decline of the Copenhagen interpretation of quantum mechanics and the recent experiments indicating that quantum mechanics does actually embody 'objective reality', one might ask if a 'mechanical', conceptual model for quantum…
In their activity, the traders approximate the rate of return by integer multiples of a minimal one. Therefore, it can be regarded as a quantized variable. On the other hand, there is the impossibility of observing the rate of return and…
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 fundamental theorem behind financial markets is that stock prices are intrinsically complex and stochastic. One of the complexities is the volatility associated with stock prices. Volatility is a tendency for prices to change…
We model the price of a stock via a Lang\'{e}vin equation with multi-dimensional fluctuations coupled in the price and in time. We generalize previous models in that we assume that the fluctuations conditioned on the time step are compound…
We study the statistical properties of volatility---a measure of how much the market is likely to fluctuate. We estimate the volatility by the local average of the absolute price changes. We analyze (a) the S&P 500 stock index for the…
The behavior of stock market returns over a period of 1-60 days has been investigated for S&P 500 and Nasdaq within the framework of nonextensive Tsallis statistics. Even for such long terms, the distributions of the returns are…
We study the temporal fluctuations in time-dependent stock prices (both individual and composite) as a stochastic phenomenon using general techniques and methods of nonequilibrium statistical mechanics. In particular, we analyze stock price…
Stable distributions is an interesting and important class of probability distributions. They were discovered explicitly by Paul L\'{e}vy in 1925 \cite{lk}. They possess many interesting properties, most importantly they are by definiton…
Price fluctuations in financial markets can be characterized by L\'evy's stable distribution, which is supported by the generalized central limit system. When the stable parameters were estimated from four different stock markets in long…
High frequency data in finance have led to a deeper understanding on probability distributions of market prices. Several facts seem to be well stablished by empirical evidence. Specifically, probability distributions have the following…
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…