  In this paper we propose a new stochastic model based on a generalization of
semi-Markov chains to study the high frequency price dynamics of traded stocks.
We assume that the financial returns are described by a weighted indexed
semi-Markov chain model. We show, through Monte Carlo simulations, that the
model is able to reproduce important stylized facts of financial time series as
the first passage time distributions and the persistence of volatility. The
model is applied to data from Italian and German stock market from first of
January 2007 until end of December 2010.
