Tuesday July 24 2012
12:00
Scuola Normale Superiore
Aula Bianchi

Bence Toth
Capital Fund Management, Paris, France

Abstract
We propose a dynamical theory of market liquidity that predicts that the average supply/demand profile is V-shaped and vanishes around the current price. This result is generic, and only relies on mild assumptions about the order flow and on the fact that prices are (to a first approximation) diffusive. This naturally accounts for two striking stylized facts: first, large metaorders have to be fragmented in order to be digested by the liquidity funnel, leading to long-memory in the sign of the order flow. Second, the anomalously small local liquidity induces a breakdown of linear response and a diverging impact of small orders, explaining the “square-root” impact law, for which we provide additional empirical support. Finally, we test our arguments quantitatively using a numerical model of order flow based on the same minimal ingredients.

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Wednesday July 18 2012
13:00
Scuola Normale Superiore
Aula 2

James G. M. Gatheral
Baruch College, The City University of New York

Abstract
In this talk we motivate the widely-used SVI (“stochastic volatility inspired”) parameterization of the implied volatility surface and show how to calibrate it in such a way as to guarantee the absence of static arbitrage. In particular, we exhibit a large class of arbitrage-free SVI volatility surfaces with a simple closed-form representation. We demonstrate the high quality of typical SVI fits with a numerical example using recent SPX options data. We conclude by suggesting that SVI might one day replace SABR as the implied volatility parameterization of choice.
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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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