Séminaire des équipes-projets

Optimal Trade Execution: Mean Variance or Mean Quadratic Variation?

  • Date : 17/07/2012
  • Lieu : Inria Paris - Rocquencourt - Antenne Parisienne, Salle Orange
  • Intervenants : Peter Forsyth, Cheriton School of Computer Science, Waterloo, Ontario
  • Organisateurs : Equipe-projet Mathrisk

Algorithmic trade execution has become a standard technique for institutional market players in recent years, particularly in the equity market where electronic trading is most prevalent. A trade execution algorithm typically seeks to execute a trade decision optimally upon receiving inputs from a human trader.

A common form of optimality criterion seeks to strike a balance between minimizing pricing impact and minimizing timing risk. For example, in the case of selling a large number of shares, a fast liquidation will cause the share price to drop, whereas a slow liquidation will expose the seller to timing risk due to the stochastic nature of the share price.

We compare optimal liquidation policies in continuous time in the presence of trading impact using numerical solutions of Hamilton Jacobi Bellman (HJB) partial differential equations (PDE). In particular, we compare the time-consistent mean-quadratic-variation strategy (Almgren and Chriss) with the time-inconsistent (pre-commitment) mean-variance strategy. The Almgren and Chriss strategy should be viewed as the industry standard.

We show that the two different risk measures lead to very different strategies and liquidation profiles.

In terms of the mean variance efficient frontier, the original Almgren/Chriss strategy is significantly sub-optimal compared to the (pre-commitment) mean-variance strategy.

This is joint work with Stephen Tse, Health Windcliff and Shannon Kenn.

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Mots-clés : Séminaire Paris - Rocquencourt MATHRISK

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