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Pré-Publication, Document De Travail Année : 2011

Optimal Portfolio Liquidation with Limit Orders

Résumé

This paper addresses the optimal scheduling of the liquidation of a portfolio using a new angle. Instead of focusing only on the scheduling aspect like Almgren and Chriss in [2], or only on the liquidity-consuming orders like Obizhaeva and Wang in [31], we link the optimal trade-schedule to the price of the limit orders that have to be sent to the limit order book to optimally liquidate a portfolio. Most practitioners address these two issues separately: they compute an optimal trading curve and they then send orders to the markets to try to follow it. The results obtained here solve simultaneously the two problems. As in a previous paper that solved the "intra-day market making problem" [19], the interactions of limit orders with the market are modeled via a Poisson process pegged to a diffusive "fair price" and a Hamilton-Jacobi-Bellman equation is used to solve the trade-off between execution risk and price risk. Backtests are finally carried out to exemplify the use of our results.
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Dates et versions

hal-00628533 , version 1 (03-10-2011)

Identifiants

  • HAL Id : hal-00628533 , version 1

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Oliver Guéant, Charles-Albert Lehalle, Joaquin Fernandez Tapia. Optimal Portfolio Liquidation with Limit Orders. 2011. ⟨hal-00628533⟩
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