  We introduce a new model for describing the fluctuations of a tick-by-tick
single asset price. Our model is based on Markov renewal processes. We consider
a point process associated to the timestamps of the price jumps, and marks
associated to price increments. By modeling the marks with a suitable Markov
chain, we can reproduce the strong mean-reversion of price returns known as
microstructure noise. Moreover, by using Markov renewal processes, we can model
the presence of spikes in intensity of market activity, i.e. the volatility
clustering, and consider dependence between price increments and jump times. We
also provide simple parametric and nonparametric statistical procedures for the
estimation of our model. We obtain closed-form formula for the mean signature
plot, and show the diffusive behavior of our model at large scale limit. We
illustrate our results by numerical simulations, and that our model is
consistent with empirical data on the Euribor future.
