  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 standard `insider
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.
