# James G. M. Gatheral, “Optimal Order Execution”

Friday July 13 2012

11:30

Scuola Normale Superiore

Aula Bianchi

**James G. M. Gatheral**

Baruch College, The City University of New York

**Abstract
**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.

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