Related papers: A Structural Model for Fluctuations in Financial M…
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…
An innovative extension of Geometric Brownian Motion model is developed by incorporating a weighting factor and a stochastic function modelled as a mixture of power and trigonometric functions. Simulations based on this Modified Brownian…
Building on a prominent agent-based model, we present a new structural stochastic volatility asset pricing model of fundamentalists vs. chartists where the prices are determined based on excess demand. Specifically, this allows for…
The present paper describes a practical example in which the probability distribution of the prices of a stock market blue chip is calculated as the wave function of a quantum particle confined in a potential well. This model may naturally…
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…
As a typical representation of complex networks studied relatively thoroughly, financial market presents some special details, such as its nonconservation and opinions spreading. In this model, agents congregate to form some clusters, which…
In this paper an arbitrage strategy is constructed for the modified Black-Scholes model driven by fractional Brownian motion or by a time changed fractional Brownian motion, when the volatility is stochastic. This latter property allows the…
Financial time series exhibit a number of interesting properties that are difficult to explain with simple models. These properties include fat-tails in the distribution of price fluctuations (or returns) that are slowly removed at longer…
We present a set of models of the main stylized facts of market price fluctuations. These models comprise dynamical evolution with threshold dynamics and Langevin price equation with multiplicative noise, percolation models to describe the…
In the Cont-Bouchaud model [cond-mat/9712318] of stock markets, percolation clusters act as buying or selling investors and their statistics controls that of the price variations. Rather than fixing the concentration controlling each…
This paper proposes a novel model of financial prices where: (i) prices are discrete; (ii) prices change in continuous time; (iii) a high proportion of price changes are reversed in a fraction of a second. Our model is analytically…
We consider a stochastic volatility model with jumps where the underlying asset price is driven by the process sum of a 2-dimensional Brownian motion and a 2-dimensional compensated Poisson process. The market is incomplete, resulting in…
We consider a tick-by-tick model of price formation, in which buy and sell orders are modeled as self-exciting point processes (Hawkes process), similar to the one in [Bacry, Delattre, Hoffmann, Muzy, Modelling microstructure noise with…
We provide simple models for the utility function (or psychology) of an actor trading a multitude of goods for money. In this framework, money has no intrinsic consumption value, but is required as a medium of exchange. A collection of such…
Financial market dynamics is rigorously studied via the exact generalized Langevin equation. Assuming market Brownian self-similarity, the market return rate memory and autocorrelation functions are derived, which exhibit an…
In the classical model of stock prices which is assumed to be Geometric Brownian motion, the drift and the volatility of the prices are held constant. However, in reality, the volatility does vary. In quantitative finance, the Heston model…
We describe a new model to simulate the dynamic interactions between market price and the decisions of two different kind of traders. They possess spatial mobility allowing to group together to form coalitions. Each coalition follows a…
In this article we discuss several aspects of the stochastic dynamics of spin models. The paper has two independent parts. Firstly, we explore a few properties of the multi-point correlations and responses of generic systems evolving in…
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…
We present several models to describe the stochastic evolution of stocks that show some strong resistance at some level and generalize to this situation the evolution based upon geometric Brownian motion. If volatility and drift are related…