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Large tick assets, i.e. assets where one tick movement is a significantfraction 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. Weintroduce a Markov-switching modeling approach for price change, where thelatent Markov process is the transition between spreads. We then use a finiteMarkov mixture of logit regressions on past squared returns to describe thedependence of the probability of price changes. The model can thus be seen as aDouble Chain Markov Model. We show that the model describes the shape of returndistribution at different time aggregations, volatility clustering, and theanomalous decrease of kurtosis of returns. We calibrate our models on Nasdaqstocks and we show that this model reproduces remarkably well the statisticalproperties of real data.

Modeling the coupled return-spread high frequency dynamics of large tick assets