Related papers: The Time Function of Stock Price
The trade of a fixed stock can be regarded as the basic process that measures its momentary price. The stock price is exactly known only at the time of sale when the stock is between traders, that is, only in the case when the owner is…
We present a time-dependent Langevin description of dynamics of stock prices. Based on a simple sliding-window algorithm, the fluctuation of stock prices is discussed in the view of a time-dependent linear restoring force which is the…
In this paper, we are interested in continuous time models in which the index level induces some feedback on the dynamics of its composing stocks. More precisely, we propose a model in which the log-returns of each stock may be decomposed…
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…
The distribution of price returns for a class of uncorrelated diffusive dynamics is considered. The basic assumptions are (1) that there is a "consensus" value associated with a stock, and (2) that the rate of diffusion depends on the…
We construct a price impact model between stocks in a correlated market. For the price change of a given stock induced by the short-run liquidity of this stock itself and of the information about other stocks, we introduce a self- and a…
This paper proposes a governing equation for stock market indexes that accounts for non-stationary effects. This is a linear Fokker-Planck equation (FPE) that describes the time evolution of the probability distribution function (PDF) of…
The present paper proposes a new framework for describing the stock price dynamics. In the traditional geometric Brownian motion model and its variants, volatility plays a vital role. The modern studies of asset pricing expand around…
A new model for the stock market price analysis is proposed. It is suggested to look at price as an everywhere discontinuous function of time of bounded variation.
Assuming that price of the underlying stock is moving in range bound, the Black-Scholes formula for options pricing supports a separation of variables. The resulting time-independent equation is solved employing different behavior of the…
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…
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…
The correlation matrix formalism is used to study temporal aspects of the stock market evolution. This formalism allows to decompose the financial dynamics into noise as well as into some coherent repeatable intraday structures. The present…
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…
We establish an analogy between the motion of spring whose mass increases linearly with time and volatile stock markets dynamics within an economic model based on simple temporal demand and supply functions [J. Phys. A: Math. Gen. 33, 3637…
A new model for the stock market price analysis is proposed. It is suggested to look at price as an everywhere discontinuous function of time of bounded variation.
What is the dominating mechanism of the price dynamics in financial systems is of great interest to scientists. The problem whether and how volatilities affect the price movement draws much attention. Although many efforts have been made,…
In the present paper we construct stock price processes with the same marginal log-normal law as that of a geometric Brownian motion and also with the same transition density (and returns' distributions) between any two instants in a given…
The Black-Scholes formula for pricing options on stocks and other securities has been generalized by Merton and Garman to the case when stock volatility is stochastic. The derivation of the price of a security derivative with stochastic…
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…