Seminar on Probability and Statistics

Seminar information archive ~02/15Next seminarFuture seminars 02/16~

Date, time & place Tuesday 13:00 - 14:10 Room #052 (Graduate School of Math. Sci. Bldg.)


13:30-14:40   Room #052 (Graduate School of Math. Sci. Bldg.)
Ioane Muni Toke (Centrale Supelec Paris)
Estimation of ratios of intensities in a Cox-type model of limit order books
[ Abstract ]
We introduce a Cox-type model for relative intensities of orders flows in a limit order book. The Cox-like intensities of the counting processes of events are assumed to share an unobserved and unspecified baseline intensity, which in finance can be identified to a global market activity affecting all events. The model is formulated in terms of relative responses of the intensities to covariates, and relative parameters can be estimated by quasi likelihood maximization. Consistency and asymptotic normality of the estimators are proven. Computationally intensive inferences are run on large samples of tick-by-tick data (35+ stocks and 220+ trading days, adding to more than one billion events). Penalization methods are also investigated. Results of the model are interpreted in terms of probability of occurrence of events. Excellent agreement with empirical data is found. Estimated model reproduces known empirical facts on imbalance, spread and queue sizes, and helps identifying trading signals of interests on a given stock.

Joint work with N.Yoshida.