相关论文: Scaling transformation and probability distributio…
We develop a scale-invariant truncated L\'evy (STL) process to describe physical systems characterized by correlated stochastic variables. The STL process exhibits L\'evy stability for the probability density, and hence shows scaling…
In this work the system of agents is applied to establish a model of the nonlinear distributed signal processing. The evolution of the system of the agents - by the prediction time scale diversified trend followers, has been studied for the…
We investigate the problem of pricing derivatives under a fractional stochastic volatility model. We obtain an approximate expression of the derivative price where the stochastic volatility can be composed of deterministic functions of time…
The statistical properties of the multipliers of the absolute returns are investigated using one-minute high-frequency data of financial time series. The multiplier distribution is found to be independent of the box size $s$ when $s$ is…
Large models have shown unprecedented capabilities in natural language processing, image generation, and most recently, time series forecasting. This leads us to ask the question: treating market prices as a time series, can large models be…
A new approach to obtaining market--directional information, based on a non-stationary solution to the dynamic equation "future price tends to the value that maximizes the number of shares traded per unit time" [1] is presented. In our…
Understanding the structure of financial markets deals with suitably determining the functional relation between financial variables. In this respect, important variables are the trading activity, defined here as the number of trades $N$,…
We consider the discretized Bachelier model where hedging is done on an equidistant set of times. Exponential utility indifference prices are studied for path-dependent European options and we compute their non-trivial scaling limit for a…
We discuss the origin of multiscaling in financial time-series and investigate how to best quantify it. Our methodology consists in separating the different sources of measured multifractality by analysing the multi/uni-scaling behaviour of…
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,…
In this paper, we establish sample path large and moderate deviation principles for log-price processes in Gaussian stochastic volatility models, and study the asymptotic behavior of exit probabilities, call pricing functions, and the…
We investigate the behavior of systems of interacting diffusion processes, known as volatility-stabilized market models in the mathematical finance literature, when the number of diffusions tends to infinity. We show that, after an…
We report evidence of a deep interplay between cross-correlations hierarchical properties and multifractality of New York Stock Exchange daily stock returns. The degree of multifractality displayed by different stocks is found to be…
We study the time evolution of a chain of nonlinear oscillators. We focus on the fractal features of the spectral entropy and analyze its characteristic intermediate timescales as a function of the nonlinear coupling. A Brownian motion is…
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.
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…
The two phase behavior in financial markets actually means the bifurcation phenomenon, which represents the change of the conditional probability from an unimodal to a bimodal distribution. In this paper, the bifurcation phenomenon in…
Large tick assets, i.e. assets where one tick movement is a significant fraction of the price and bid-ask spread is almost always equal to one tick, display a dynamics in which price changes and spread are strongly coupled. We introduce a…
We investigate financial market correlations using random matrix theory and principal component analysis. We use random matrix theory to demonstrate that correlation matrices of asset price changes contain structure that is incompatible…
Correlations in multifractal series have been investigated, extensively. Almost all approaches try to find scaling features of a given time series. However, the analysis of such scaling properties has some difficulties such as finding a…