2,280 research outputs found
Heavy-tailed Distributions In Stochastic Dynamical Models
Heavy-tailed distributions are found throughout many naturally occurring
phenomena. We have reviewed the models of stochastic dynamics that lead to
heavy-tailed distributions (and power law distributions, in particular)
including the multiplicative noise models, the models subjected to the
Degree-Mass-Action principle (the generalized preferential attachment
principle), the intermittent behavior occurring in complex physical systems
near a bifurcation point, queuing systems, and the models of Self-organized
criticality. Heavy-tailed distributions appear in them as the emergent
phenomena sensitive for coupling rules essential for the entire dynamics
Simulating and analyzing order book data: The queue-reactive model
Through the analysis of a dataset of ultra high frequency order book updates,
we introduce a model which accommodates the empirical properties of the full
order book together with the stylized facts of lower frequency financial data.
To do so, we split the time interval of interest into periods in which a well
chosen reference price, typically the mid price, remains constant. Within these
periods, we view the limit order book as a Markov queuing system. Indeed, we
assume that the intensities of the order flows only depend on the current state
of the order book. We establish the limiting behavior of this model and
estimate its parameters from market data. Then, in order to design a relevant
model for the whole period of interest, we use a stochastic mechanism that
allows for switches from one period of constant reference price to another.
Beyond enabling to reproduce accurately the behavior of market data, we show
that our framework can be very useful for practitioners, notably as a market
simulator or as a tool for the transaction cost analysis of complex trading
algorithms
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