Statistical Modelling 6 (2006), 97–118
Estimation and filtering by reversible jump MCMC
for a doubly stochastic Poisson model for
ultra-high-frequency financial data
S. Centanni
Department of Economics, Finance and Statistics,
University of Perugia,
Perugia
Italy
M. Minozzo
Department of Economics, Finance and Statistics,
University of Perugia,
Via A. Pascoli,
I–06100 Perugia
Italy
eMmail: minozzo@stat.unipg.it
Abstract:
We propose a modeling framework for ultra-high-frequency
data on financial asset price movements.
The models proposed belong to the class of the doubly
stochastic Poisson processes with marks and
allow an interpretation of the changes in price volatility
and trading activity in terms of news or information
arrival. Assuming that the intensity process underlying
event arrivals is unobserved by market agents,
we propose a signal extraction (filtering) method based
on the reversible jump Markov chain Monte Carlo
algorithm. Moreover, given a realization of the price
process, inference on the parameters can be performed
by appealing to stochastic versions of the
expectation–maximization algorithm. The simulation methods
proposed will be applied to the computation of hedging
strategies and derivative prices.
Keywords:
intraday data; marked point processes; news arrival;
option pricing; stochastic EM algorithm
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