Motivated by the empirical analysis of market data, two structural relationships are proposed and studied for high frequency markets. The first is a self-financing wealth equation in which the trader's wealth is decomposed into three components: frictionless wealth, transaction costs and instantaneous adverse selection. The second relationship quantifies this instantaneous adverse selection. We derive these relationships theoretically and tests them on empirical data. We conclude by deriving their continuous time counterpart and two applications to option pricing and market making under transaction costs and price impact.
Back to Workshop II: The Mathematics of High Frequency Financial Markets: Limit Order Books, Frictions, Optimal Execution and Program Trading