From asymptotic properties of general point processes to the ranking of financial agents

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.

Optimal make take fees in a multi market maker environment

“…The case of a single market maker means that he has no competitor, hence only needs to manage his inventory risk. However, for many financial assets, market making activity is provided by several market makers (typically three to ten), see for example [15]. Therefore, having a multi agents model suits better to the vast majority of markets.…”