Related papers: Hitting Time Distributions in Financial Markets
We compare the probability distribution of returns for the three major stock-market indexes (Nasdaq, S&P500, and Dow-Jones) with an analytical formula recently derived by Dragulescu and Yakovenko for the Heston model with stochastic…
We study the Heston model, where the stock price dynamics is governed by a geometrical (multiplicative) Brownian motion with stochastic variance. We solve the corresponding Fokker-Planck equation exactly and, after integrating out the…
We shortly review the statistical properties of the escape times, or hitting times, for stock price returns by using different models which describe the stock market evolution. We compare the probability function (PF) of these escape times…
We present a phenomenological study of stock price fluctuations of individual companies. We systematically analyze two different databases covering securities from the three major US stock markets: (a) the New York Stock Exchange, (b) the…
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…
This paper builds a model of high-frequency equity returns by separately modeling the dynamics of trade-time returns and trade arrivals. Our main contributions are threefold. First, we characterize the distributional behavior of…
We study the price dynamics of stocks traded in a financial market by considering the statistical properties both of a single time series and of an ensemble of stocks traded simultaneously. We use the $n$ stocks traded in the New York Stock…
We show that the moments of the distribution of historic stock returns are in excellent agreement with the Heston model and not with the multiplicative model, which predicts power-law tails of volatility and stock returns. We also show that…
An analytical formula for the probability distribution of stock-market returns, derived from the Heston model assuming a mean-reverting stochastic volatility, was recently proposed by Dragulescu and Yakovenko in Quantitative Finance 2002.…
We study the mean escape time in a market model with stochastic volatility. The process followed by the volatility is the Cox Ingersoll and Ross process which is widely used to model stock price fluctuations. The market model can be…
We study the asymptotic behavior of distribution densities arising in stock price models with stochastic volatility. The main objects of our interest in the present paper are the density of time averages of the squared volatility process…
In financial markets, greater volatility is usually considered synonym of greater risk and instability. However, large market downturns and upturns are often preceded by long periods where price returns exhibit only small fluctuations. To…
In financial markets, not only prices and returns can be considered as random variables, but also the waiting time between two transactions varies randomly. In the following, we analyse the statistical properties of General Electric stock…
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…
A statistical physics model for the time evolutions of stock portfolios is proposed. In this model the time series of price changes are coded into the sequences of up and down spins. The Hamiltonian of the system is introduced and is…
We consider uncorrelated Stein-Stein, Heston, and Hull-White models and their perturbations by compound Poisson processes with jump amplitudes distributed according to a double exponential law. Similar perturbations of the Black-Scholes…
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…
We study in this paper the time evolution of stock markets using a statistical physics approach. Each agent is represented by a spin having a number of discrete states $q$ or continuous states, describing the tendency of the agent for…
Price movements of stock market are not totally random. In fact, what drives the financial market and what pattern financial time series follows have long been the interest that attracts economists, mathematicians and most recently computer…
We analyze the Standard & Poor's 500 stock market index from the last 22 years. The probability density function of price returns exhibits two well-distinguished regimes with self-similar structure: the first one displays strong…