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Just published on arxiv:

From asymptotic properties of general point processes to the ranking of financial agents by Othmane Mounjid, Mathieu Rosenbaum and Pamela Saliba

Abstract: We propose a general non-linear order book model that is built from the individual behaviours of the agents. Our framework encompasses Markovian and Hawkes based models. Under mild assumptions, we prove original results on the ergodicity and diffusivity of such system. Then we provide closed form formulas for various quantities of interest: stationary distribution of the best bid and ask quantities, spread, liquidity fluctuations and price volatility. These formulas are expressed in terms of individual order flows of market participants. Our approach enables us to establish a ranking methodology for the market makers with respect to the quality of their trading.

Just published on arxiv:

Optimal auction duration: A price formation viewpoint by Paul Jusselin, Thibaut Mastrolia, Mathieu Rosenbaum

Abstract: We consider an auction market in which market makers fill the order book during a given time period while some other investors send market orders. We define the clearing price of the auction as the price maximizing the exchanged volume at the clearing time according to the supply and demand of each market participants. Then we derive in a semi-explicit form the error made between this clearing price and the fundamental price as a function of the auction duration. We study the impact of the behavior of market takers on this error. To do so we consider the case of naive market takers and that of rational market takers playing a Nash equilibrium to minimize their transaction costs. We compute the optimal duration of the auctions for 77 stocks traded on Euronext and compare the quality of price formation process under this optimal value to the case of a continuous limit order book. Continuous limit order books are found to be usually sub-optimal. However, in term of our metric, they only moderately impair the quality of price formation process. Order of magnitude of optimal auction durations is from 2 to 10 minutes.

New paper by Pamela Saliba: The information content of high frequency traders aggressive orders: recent evidences:

Abstract

This empirical study uses a unique recent data set provided by the French regulator “Autorité des Marchés Financiers” and gives some evidence concerning the impact of aggressive orders on the price formation process and the information content of these orders according to the different order flow categories (high frequency traders, agency participants and proprietary participants). As expected, we find that the price impact of aggressive orders consuming exactly the quantity present at the best limit is higher than that of the ones consuming less than the quantity present at the best limit. Furthermore, the price impact is an increasing function with respect to the consumed share in percentage. We show that these price impact disparities are sustainable over time: both price impacts are permanent. On the contrary, the impact of orders consuming more than the quantity present at the best limit starts to diminish one second after the aggressive order. In contrast to previous literature, we find that the aggressive orders of HFTs are more informed than the ones of agency and proprietary members. This new finding may be an indicator of the evolution of high frequency traders activity over the years.

New paper out at arxiv:

From Glosten-Milgrom to the whole limit order book and applications to financial regulation

Abstract:

We build an agent-based model for the order book with three types of market participants: informed trader, noise trader and competitive market makers. Using a Glosten-Milgrom like approach, we are able to deduce the whole limit order book (bid-ask spread and volume available at each price) from the interactions between the different agents. More precisely, we obtain a link between efficient price dynamic, proportion of trades due to the noise trader, traded volume, bid-ask spread and equilibrium limit order book state. With this model, we provide a relevant tool for regulators and market platforms. We show for example that it allows us to forecast consequences of a tick size change on the microstructure of an asset. It also enables us to value quantitatively the queue position of a limit order in the book.