STATIONARY DISTRIBUTION OF THE VOLUME AT THE BEST QUOTE IN A POISSON ORDER BOOK MODEL

Ioane Muni Toke (1, 2)

1 FiQuant - Chaire de finance quantitative
2 MICS - Mathématiques et Informatique pour la Complexité et les Systèmes

We develop a Markovian model that deals with the volume offered at the best quote of an electronic order book. The volume of the first limit is a stochastic process whose paths are periodically interrupted and reset to a new value, either by a new limit order submitted inside the spread or by a market order that removes the first limit. Using applied probability results on killing and resurrecting Markov processes, we derive the stationary distribution of the volume offered at the best quote. All proposed models are empirically fitted and compared, stressing the importance of the proposed mechanisms.

Keywords: aggressive limit orders; volume of the best quote; limit order book; aggressive market orders; killing and resurrecting Markov processes

Domains: Trading and Market Microstructure [q-fin.TR]; Statistical Finance [q-fin.ST]

Ioane Muni Toke. STATIONARY DISTRIBUTION OF THE VOLUME AT THE BEST QUOTE IN A POISSON ORDER BOOK MODEL. International Journal of Theoretical and Applied Finance, 2017, 20 (06), pp.1750039. ⟨10.1142/S021902491750039X⟩. ⟨hal-01705085⟩