Friday July 13 2012
Scuola Normale Superiore
James G. M. Gatheral
Baruch College, The City University of New York
We review various models of market impact. We use variational calculus to derive optimal execution strategies, noting that in many conventional models, static strategies are dynamically optimal. We then present a model in which the optimal strategy does depend on the stock price and derive an explicit closed-form solution for this strategy by solving the HJB equation. We discuss price manipulation, indicating modeling choices for which this is unlikely to be a problem. We present empirical evidence and some heuristic arguments justifying the well-known square-root formula for market impact. Assuming price dynamics that are consistent with the square-root formula, we suggest likely properties of optimal execution strategies.