The microstructure of high frequency markets

Abstract: We present a novel approach to describing the microstructure of high frequency trading using two key elements. First we introduce a new notion of informed trader which we starkly contrast to current informed trader models. We describe the exact nature of the superior information' high frequency traders have access to, and how these agents differ from the more standardinsider traders' described in past papers. This then leads to a model and an empirical analysis of the data which strongly supports our claims. The second key element is a rigorous description of clearing conditions on a limit order book and how to derive correct formulas for such a market. From a theoretical point of view, this allows the exact identification of two frictions in the market, one of which is intimately linked to our notion of `superior information'. Empirically, we show that ignoring these frictions can misrepresent the wealth exchanged on the market by 50%. Finally, we showcase two applications of our approach: we measure the profits made by high frequency traders on NASDAQ and re-visit the standard Black - Scholes model to determine how trading frictions alter the delta-hedging strategy.