  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 Markov-switching modeling approach for price change, where the
latent Markov process is the transition between spreads. We then use a finite
Markov mixture of logit regressions on past squared returns to describe the
dependence of the probability of price changes. The model can thus be seen as a
Double Chain Markov Model. We show that the model describes the shape of return
distribution at different time aggregations, volatility clustering, and the
anomalous decrease of kurtosis of returns. We calibrate our models on Nasdaq
stocks and we show that this model reproduces remarkably well the statistical
properties of real data.
