arXiv research

We statistically investigate the distribution of share price and the distributions of three common financial indicators using data from approximately 8,000 companies publicly listed worldwide for the period 2004-2013. We find that the distribution of share price follows Zipf's law; that is, it can be approximated by a …

This paper explains how predictable order flow can lead to Brownian motion in financial prices.

In this paper, we describe a newly discovered statistical property of time series data for daily price changes. We conducted quantitative investigation of the {\it calm-time intervals} of price changes for 800 companies listed in the Tokyo Stock Exchange, and for the Nikkei 225 index over a 27-year period from January …

In a recent Nature paper, Gabaix et al. \cite{Gabaix03} presented a theory to explain the power law tail of price fluctuations. The main points of their theory are that volume fluctuations, which have a power law tail with exponent roughly -1.5, are modulated by the average market impact function, which describes the r…

It is now well established empirically that financial price changes are distributed according to a power law, with cubic exponent. This is a fascinating regularity, as it holds for various classes of securities, on various markets, and on various time scales. The universality of this law suggests that there must be som…

Paper finds linear laws in Bitcoin price changes, aiding anomaly detection.

I consider the problem of the optimal limit order price of a financial asset in the framework of the maximization of the utility function of the investor. The analytical solution of the problem gives insight on the origin of the recently empirically observed power law distribution of limit order prices. In the framewor…

We study the rank distribution, the cumulative probability, and the probability density of returns of stock prices of listed firms traded in four stock markets. We find that the rank distribution and the cumulative probability of stock prices traded in are consistent approximately with the Zipf's law or a power law. It…

Study classifies stock price jumps as exogenous or endogenous using news data.

In this paper, we quantitatively investigate the statistical properties of a statistical ensemble of stock prices. We selected 1200 stocks traded on the Tokyo Stock Exchange, and formed a statistical ensemble of daily stock prices for each trading day in the 3-year period from January 4, 1999 to December 28, 2001, corr…

In this paper, we quantitatively investigate the properties of a statistical ensemble of stock prices. We focus attention on the relative price defined as $X(t) = S(t)/S(0)$, where $S(0)$ is the initial price. We selected approximately 3200 stocks traded on the Japanese Stock Exchange and formed a statistical ensem…

This paper investigates the rank distribution, cumulative probability, and probability density of price returns for the stocks traded in the KSE and the KOSDAQ market. This research demonstrates that the rank distribution is consistent approximately with the Zipf's law with exponent $α= -1.00$ (KSE) and -1.31 (KOSDAQ),…

The importance of the power law has been well realized in econophysics over the last decade. For instance, the distribution of the rate of stock price variation and of personal assets show the power law. While these results reveal the striking scale invariance of financial markets, the behaviour of price in real econom…

In this paper we present an analysis of power law statistics on land markets. There have been no other studies that have analyzed power law statistics on land markets up to now. We analyzed a database of the assessed value of land, which is officially monitored and made available to the public by the Ministry of Land, …

In this article we consider the problem of giving a robust, model-independent, lower bound on the price of a forward starting straddle with payoff $|F_{T_1} - F_{T_0}|$ where $0<T_0<T_1$. Rather than assuming a model for the underlying forward price $(F_t)_{t \geq 0}$, we assume that call prices for maturities $T_0<T_1…

The paper proves the law of one price in a continuous-time setting without friction.

We respond to the issues discussed by Farmer and Lillo (FL) related to our proposed approach to understanding the origin of power-law distributions in stock price fluctuations. First, we extend our previous analysis to 1000 US stocks and perform a new estimation of market impact that accounts for splitting of large ord…

Study finds price impact follows a 'double' square-root law, suggesting mechanical origin.

Statistical properties of an order book and the effect they have on price dynamics were studied using the high-frequency NASDAQ Level II data. It was observed that the size distribution of marketable orders (transaction sizes) has power law tails with an exponent 1+mu_{market}=2.4 \pm 0.1. The distribution of limit ord…

Study reveals that cryptocurrency price variations follow power-law distributions, influenced by age and market capitalization.

The paper solves classical problems in option pricing.

Study confirms the square-root law in price impact across Tokyo stocks.

The bitcoin price has surged in recent years and it has also exhibited phases of rapid decay. In this paper we address the question to what extent this novel cryptocurrency market can be viewed as a classic or semi-efficient market. Novel and robust tools for estimation of multi-fractal properties are used to show that…

In this paper we investigate quantitatively statistical properties of ensemble of {\it land prices} in Japan in the period from 1981 to 2002, corresponding to the period of bubbles and crashes. We find that the tail of the distributions of ensembles of the land prices in the high price range is well described by a powe…

In this paper we quantitatively investigate the statistical properties of an ensemble of {\it stock prices}. We selected 1200 stocks traded in the Tokyo Stock Exchange and formed a statistical ensemble of daily stock prices for each trading day in the 5 year period from January 4, 1988 to December 30, 1992. We found th…

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 and denominator and their correlation. We also obtain the conditional probability…

We introduce a simple generalization of rational bubble models which removes the fundamental problem discovered by [Lux and Sornette, 1999] that the distribution of returns is a power law with exponent less than 1, in contradiction with empirical data. The idea is that the price fluctuations associated with bubbles mus…

Two price regimes identified in limit order books: close and far from quotes.

We introduce solvable stochastic dealer models, which can reproduce basic empirical laws of financial markets such as the power law of price change. Starting from the simplest model that is almost equivalent to a Poisson random noise generator, the model becomes fairly realistic by adding only two effects, the self-mod…

Algorithm generates realistic metaorders from public trade data.

Bitcoin returns exhibit a distinct inverse cubic law scaling behavior.

We propose an artificial market model based on deterministic agents. The agents modify their ask/bid price depending on past price changes. The temporal development of market price fluctuations is calculated numerically. A probability density function of market price changes has power law tails. Autocorrelation coeffic…

We introduce an autoregressive-type model of prices in financial market taking into account the self-modulation effect. We find that traders are mainly using strategies with weighted feedbacks of past prices. These feedbacks are responsible for the slow diffusion in short times, apparent trends and power law distributi…

LLT improves cryptocurrency price movement prediction accuracy.

The author proposes a finance trading strategy named Entropy Oriented Trading and apply thermodynamics on the strategy. The state variables are chosen so that the strategy satisfies the second law of thermodynamics. Using the law, the author proves that the rate of investment (ROI) of the strategy is equal to or more t…

Bayesian theory explains market impact of large trades.

We build a methodology that takes a given option price in the tails with strike $K$ and extends (for calls, all strikes > $K$, for puts all strikes $< K$) assuming the continuation falls into what we define as "Karamata Constant" over which the strong Pareto law holds. The heuristic produces relative prices for options…

The probability distribution of stock price changes is studied by analyzing a database (the Trades and Quotes Database) documenting every trade for all stocks in three major US stock markets, for the two year period Jan 1994 -- Dec 1995. A sample of 40 million data points is extracted, which is substantially larger tha…

Study uses OT to simulate markets, revealing power-law returns are driven by informational effect.

Recently, Mike and Farmer have constructed a very powerful and realistic behavioral model to mimick the dynamic process of stock price formation based on the empirical regularities of order placement and cancelation in a purely order-driven market, which can successfully reproduce the whole distribution of returns, not…

The observation of power laws in the time to extrema of volatility, volume and intertrade times, from milliseconds to years, are shown to result straightforwardly from the selection of biased statistical subsets of realizations in otherwise featureless processes such as random walks. The bias stems from the selection o…

The nature of fluctuations in the Indian financial market is analyzed in this paper. We have looked at the price returns of individual stocks, with tick-by-tick data from the National Stock Exchange (NSE) and daily closing price data from both NSE and the Bombay Stock Exchange (BSE), the two largest exchanges in India.…

The paper uncovers two key laws of market impact influenced by volume and participation rate.

Financial markets can be seen as complex systems in non-equilibrium steady state, one of whose most important properties is the distribution of price fluctuations. Recently, there have been assertions that this distribution is qualitatively different in emerging markets as compared to developed markets. Here we analyse…

The use of kinetic modelling based on partial differential equations for the dynamics of stock price formation in financial markets is briefly reviewed. The importance of behavioral aspects in market booms and crashes and the role of agents' heterogeneity in emerging power laws for price distributions is emphasized and…

This paper studies a limit order book (LOB) model, in which the order dynamics depend on both, the current best available prices and the current volume density functions. For the joint dynamics of the best bid price, the best ask price, and the standing volume densities on both sides of the LOB we derive a weak law of …

We introduce a deterministic dealer model which implements most of the empirical laws, such as fat tails in the price change distributions, long term memory of volatility and non-Poissonian intervals. We also clarify the causality between microscopic dealers' dynamics and macroscopic market's empirical laws.

Based on the order flow data of a stock and its warrant, the immediate price impacts of market orders are estimated by two competitive models, the power-law model (PL model) and the logarithmic model (LG model). We find that the PL model is overwhelmingly superior to the LG model, regarding the robustness of the estima…