Semi Markov Model for Market Microstructure

25 Pages Posted: 6 May 2013

See all articles by Pietro Fodra

Pietro Fodra

Université Paris VII Denis Diderot

Huyên Pham

Université de Paris

Date Written: May 6, 2013


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 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 find that our model is consistent with empirical data on the Euribor future.

Keywords: Microstructure noise, High-frequency data, Markov renewal process, Signature plot, Scaling limit

JEL Classification: G10, C51

Suggested Citation

Fodra, Pietro and Pham, Huyen, Semi Markov Model for Market Microstructure (May 6, 2013). Available at SSRN: or

Pietro Fodra

Université Paris VII Denis Diderot ( email )

2, place Jussieu
Paris, 75005

Huyen Pham (Contact Author)

Université de Paris ( email )

Batiment Sophie Germain 5 rue Thomas Mann
Paris, 75205

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