Optimal execution strategies in limit order books with general shape functions

Quantitative Finance (Impact Factor: 0.82). 08/2007; DOI: 10.2139/ssrn.1510104
Source: OAI

ABSTRACT We consider optimal execution strategies for block market orders placed in a limit order book (LOB). We build on the resilience model proposed by Obizhaeva and Wang (2005) but allow for a general shape of the LOB defined via a given density function. Thus, we can allow for empirically observed LOB shapes and obtain a nonlinear price impact of market orders. We distinguish two possibilities for modeling the resilience of the LOB after a large market order: the exponential recovery of the number of limit orders, i.e., of the volume of the LOB, or the exponential recovery of the bid-ask spread. We consider both of these resilience modes and, in each case, derive explicit optimal execution strategies in discrete time. Applying our results to a block-shaped LOB, we obtain a new closed-form representation for the optimal strategy, which explicitly solves the recursive scheme given in Obizhaeva and Wang (2005). We also provide some evidence for the robustness of optimal strategies with respect to the choice of the shape function and the resilience-type.

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    ABSTRACT: We consider a framework for solving optimal liquidation problems in limit order books. In particular, order arrivals are modeled as a point process whose intensity depends on the liquidation price. We set up a stochastic control problem in which the goal is to maximize the expected revenue from liquidating the entire position held. We solve this optimal liquidation problem for power-law and exponential-decay order book models and discuss several extensions. We also consider the continuous selling (or fluid) limit when the trading units are ever smaller and the intensity is ever larger. This limit provides an analytical approximation to the value function and the optimal solution. Using techniques from viscosity solutions we show that the discrete state problem and its optimal solution converge to the corresponding quantities in the continuous selling limit uniformly on compacts.
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    ABSTRACT: In limit order book markets, traders face the problem whether to display or hide their orders. While hiding reduces exposure impact, exposing can increase execution priority. Based on order flow dynamics, we develop a structural model that captures this trade-off. A central aspect of this work is the market impact of exposure: exposed limit orders affect incoming order flow. We derive explicit characterizations of the optimal exposure strategy under various market specifications. Using high-resolution ITCH data, we estimate the true impact of the exposure and calculate the optimal exposure for various stocks under high-frequency trading horizons. It turns out that exposure does mainly affect the supply side of liquidity. Our results suggests that the use of hidden orders can significantly increase trade performance.
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