Related papers: Using the Scaling Analysis to Characterize Financi…
We conduct cluster analysis on a class of locally asymptotically self-similar stochastic processes, which includes multifractional Brownian motion as a representative. When the true number of clusters is supposed to be known, a new…
Earlier we proposed the stochastic point process model, which reproduces a variety of self-affine time series exhibiting power spectral density S(f) scaling as power of the frequency f and derived a stochastic differential equation with the…
The multifractal structure of the temporal dependence of the Deutsche Aktienindex (DAX) is analyzed. The $q$-th order moments of the structure functions and the singular measures are calculated. The generalized Hurst exponent $H(q)$ and the…
Using simple particle models of limit order markets, we argue that mid-term over-diffusive price behaviour is inherent to the very nature of these markets. Several rules for rate changes are considered. We obtain analytical results for…
Following a Geometrical Brownian Motion extension into an Irrational Fractional Brownian Motion model, we re-examine agent behaviour reacting to time dependent news on the log-returns thereby modifying a financial market evolution. We…
In this paper, three approaches to calculate the self-similarity exponent of a time series are compared in order to determine which one performs best to identify the transition from random efficient market behavior (EM) to herding behavior…
This paper studies the time-varying structure of the equity market with respect to market capitalization. First, we analyze the distribution of the 100 largest companies' market capitalizations over time, in terms of inequality,…
We study theoretical and empirical aspects of the mean exit time of financial time series. The theoretical modeling is done within the framework of continuous time random walk. We empirically verify that the mean exit time follows a…
Modeling financial data often relies on assumptions that may prove insufficient or unrealistic in practice. The Geometric Brownian Motion (GBM) model is frequently employed to represent stock price processes. This study investigates whether…
In this article we look at stochastic processes with uncertain parameters, and consider different ways in which information is obtained when carrying out observations. For example we focus on the case of a the random evolution of a traded…
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…
A central problem of Quantitative Finance is that of formulating a probabilistic model of the time evolution of asset prices allowing reliable predictions on their future volatility. As in several natural phenomena, the predictions of such…
Multivariate probability density functions of returns are constructed in order to model the empirical behavior of returns in a financial time series. They describe the well-established deviations from the Gaussian random walk, such as an…
This paper proposes an enhanced approach to modeling and forecasting volatility using high frequency data. Using a forecasting model based on Realized GARCH with multiple time-frequency decomposed realized volatility measures, we study the…
A new model for stocks markets using integer values for each stock price is presented. In contrast with previously reported models, the variables used in the model are not of binary type, but of more general integer type. It is shown how…
The financial market is nonpredictable, as according to the Bachelier, the mathematical expectation of the speculator is zero. Nevertheless, we observe in the price fluctuations the two distinct scales, short and long time. Behaviour of a…
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 consider a financial market where the asset price follows a fractional Brownian motion. We introduce a family of investment strategies, and quantify profit possibilities for both persistent and antipersistant markets.
Complex systems comprise a large number of interacting elements, whose dynamics is not always a priori known. In these cases -- in order to uncover their key features -- we have to turn to empirical methods, one of which was recently…
This study investigates empirically whether the degree of stock market efficiency is related to the prediction power of future price change using the indices of twenty seven stock markets. Efficiency refers to weak-form efficient market…