Discussion Paper Series 2010-E-25

Optimal Execution of Multiasset Block Orders under Stochastic Liquidity

Naoki Makimoto, Yoshihiko Sugihara

In this paper, we develop a multiasset model of market liquidity and derive the optimal strategy for block order execution under both liquidity and volatility risk. The market liquidity flowing into and out of an order book is modeled as a mean-reverting stochastic process. Given the shape of the order book for each asset, we express the market impact of an execution as a recursive impact that recovers gradually with associated uncertainty. We then derive the optimal execution strategy as a closed-form solution to the mean-variance problem that optimizes the trade-off between the market impact and the volatility/liquidity risk given investor risk aversion. Using our model, we analyze some implications of the optimal execution strategy with comparative statics and simulations. We also discuss whether we avoid price manipulation with our optimal execution strategy.

Keywords: optimal execution strategy; market impact; transaction cost; stochastic liquidity; limit order book; price manipulation; mean-variance optimization

Views expressed in the paper are those of the authors and do not necessarily reflect those of the Bank of Japan or Institute for Monetary and Economic Studies.

Copyright © 2010 Bank of Japan All Rights Reserved.

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