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Title: Intensity ratios of marked point processes for limit order book modeling Authors:  Ioane Muni Toke - CentraleSupelec (France) [presenting]
Abstract: A multidimensional point process with ``Cox-type'' intensities is considered. Given $\lambda_0(t)$ is an unobserved unspecified stochastic baseline intensity, and the $X_j$'s are observable covariate processes, the intensity of the $i$th coordinate process is $\lambda^i(t)=\lambda_0(t)\exp\left(\sum_{j} \vartheta^i_j X_j(t)\right)$. In a previous work, we have proposed an estimation procedure of the parameters $\theta^i_j=\vartheta^i_j-\vartheta^0_j$ based on the quasi-likelihood of intensity ratios. Quasi-maximum likelihood estimators of $\theta^i_j$'s are consistent and asymptotically normal. This framework is suitable to model high-frequency order flows on a financial exchange. It provides a meaningful modeling of order submission intensities, an assessment of trading signals, and may have good prediction properties. We now extend the previous framework to the case of marked point processes. We are thus able to model arrivals of orders in a limit order book along with their size. We propose a multi-step ratio estimation procedure to sign market orders and determine whether they lead to a price change. The fitted model is able to provide out-of-sample predictions of the sign of the next price change (in a theoretical setting without any latency, computational cost or trading costs).