Related papers: A Theory of Fluctuations in Stock Prices
The principle of absence of arbitrage opportunities allows obtaining the distribution of stock price fluctuations by maximizing its information entropy. This leads to a physical description of the underlying dynamics as a random walk…
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…
The volatility characterizes the amplitude of price return fluctuations. It is a central magnitude in finance closely related to the risk of holding a certain asset. Despite its popularity on trading floors, the volatility is unobservable…
What return should you expect when you take on a given amount of risk? How should that return depend upon other people's behavior? What principles can you use to answer these questions? In this paper, we approach these topics by exploring…
We study the dependence of volatility on the stock price in the stochastic volatility framework on the example of the Heston model. To be more specific, we consider the conditional expectation of variance (square of volatility) under fixed…
In order to investigate the origin of large price fluctuations, we analyze stock price changes of ten frequently traded NASDAQ stocks in the year 2002. Though the influence of the trading frequency on the aggregate return in a certain time…
We explore a decomposition in which returns on a large class of portfolios relative to the market depend on a smooth non-negative drift and changes in the asset price distribution. This decomposition is obtained using general continuous…
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…
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…
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 new theory for pricing options of a stock is presented. It is based on the assumption that while successive variations in return are uncorrelated, the frequency with which a stock is traded depends on the value of the return. The solution…
Stock prices are known to exhibit non-Gaussian dynamics, and there is much interest in understanding the origin of this behavior. Here, we present a model that explains the shape and scaling of the distribution of intraday stock price…
We investigated distributions of short term price trends for high frequency stock market data. A number of trends as a function of their lengths was measured. We found that such a distribution does not fit to results following from an…
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 investigate the general problem of how to model the kinematics of stock prices without considering the dynamical causes of motion. We propose a stochastic process with long-range correlated absolute returns. We find that the model is…
Several models of stock trading [P. Bak et al, Physica A {\bf 246}, 430 (1997)] are analyzed in analogy with one-dimensional, two-species reaction-diffusion-branching processes. Using heuristic and scaling arguments, we show that the…
We investigate the random walk of prices by developing a simple model relating the properties of the signs and absolute values of individual price changes to the diffusion rate (volatility) of prices at longer time scales. We show that this…
The paper proposes a class of financial market models which are based on inhomogeneous telegraph processes and jump diffusions with alternating volatilities. It is assumed that the jumps occur when the tendencies and volatilities are…
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…
This paper proposes a theory of stock market predictability patterns based on a model of heterogeneous beliefs. In a discrete finite time framework, some agents receive news about an asset's fundamental value through a noisy signal. The…