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The scaling properties of oil price fluctuations are described as a non-stationary stochastic process realized by a time series of finite length. An original model is used to extract the scaling exponent of the fluctuation functions within…

We present cross and time series analysis of price fluctuations in the U.S. Treasury fixed income market. By means of techniques borrowed from statistical physics we show that the correlation among bonds depends strongly on the maturity and…

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…

The concepts of scale invariance, self-similarity and scaling have been fruitfully applied to the study of price fluctuations in financial markets. After a brief review of the properties of stable Levy distributions and their applications…

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…

We consider the problem of valuation of American options written on dividend-paying assets whose price dynamics follows a multidimensional exponential Levy model. We carefully examine the relation between the option prices, related partial…

We study the work fluctuations of a particle subjected to a deterministic drag force plus a random forcing whose statistics is of the L\'evy type. In the stationary regime, the probability density of the work is found to have ``fat''…

Single index financial market models cannot account for the empirically observed complex interactions between shares in a market. We describe a multi-share financial market model and compare characteristics of the volatility, that is the…

Fluctuation properties of the Langevin equation including a multiplicative, power-law noise and a quadratic potential are discussed. The noise has the Levy stable distribution. If this distribution is truncated, the covariance can be…

The dynamics of prices in financial markets has been studied intensively both experimentally (data analysis) and theoretically (models). Nevertheless, a complete stochastic characterization of volatility is still lacking. What it is well…

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…

Multiplicity fluctuations and correlations are calculated within thermalized relativistic ideal quantum gases. These are shown to be sensitive to the choice of statistical ensemble as well as to the choice of acceptance window in momentum…

Based on the tick-by-tick stock prices from the German and American stock markets, we study the statistical properties of the distribution of the individual stocks and the index returns in highly collective and noisy intervals of trading,…

In this third paper of the series, which started with [N. P. Bailey et al., J. Chem. Phys. 129, 184507 and 184508 (2008)], we continue the development of the theoretical understanding of strongly correlating liquids - those whose…

We give a stochastic microscopic modelling of stock markets driven by continuous double auction. If we take into account the mimetic behavior of traders, when they place limit order, our virtual markets shows the power-law tail of the…

We consider a stochastic volatility model where the dynamics of the volatility are given by a possibly infinite linear combination of the elements of the time extended signature of a Brownian motion. First, we show that the model is…

Analogies between the price dynamics in the foreign exchange market and 3-dimensional fully developed turbulence were recently presented in Nature vol. 381, 767-769 (1996). Independently, we have carried out a study comparing the parallel…

Financial time series exhibit two different type of non linear correlations: (i) volatility autocorrelations that have a very long range memory, on the order of years, and (ii) asymmetric return-volatility (or `leverage') correlations that…

We investigate the correlation properties of transaction data from the New York Stock Exchange. The trading activity f(t) of each stock displays a crossover from weaker to stronger correlations at time scales 60-390 minutes. In both…

We present an empirical study of the subordination hypothesis for a stochastic time series of a stock price. The fluctuating rate of trading is identified with the stochastic variance of the stock price, as in the continuous-time random…