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Optimal Execution of Multiasset Block Orders under Stochastic Liquidity

Author

Listed:
  • Naoki Makimoto

    (Professor, Graduate School of Business Sciences, University of Tsukuba (E-mail: makimoto@gssm.gsbs.tsukuba.ac.jp))

  • Yoshihiko Sugihara

    (Deputy Director and Economist, Institute for Monetary and Economic Studies, Bank of Japan (E-mail: yoshihiko.sugihara@boj.or.jp))

Abstract

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.

Suggested Citation

  • Naoki Makimoto & Yoshihiko Sugihara, 2010. "Optimal Execution of Multiasset Block Orders under Stochastic Liquidity," IMES Discussion Paper Series 10-E-25, Institute for Monetary and Economic Studies, Bank of Japan.
    • Handle: RePEc:ime:imedps:10-e-25
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    File URL: http://www.imes.boj.or.jp/research/papers/english/10-E-25.pdf
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    Cited by:

    1. Kensuke Ishitani & Takashi Kato, 2015. "Theoretical and Numerical Analysis of an Optimal Execution Problem with Uncertain Market Impact," Papers 1506.02789, arXiv.org, revised Aug 2015.
    2. Takashi Kato, 2011. "An Optimal Execution Problem with a Geometric Ornstein-Uhlenbeck Price Process," Papers 1107.1787, arXiv.org, revised Jul 2014.

    More about this item

    Keywords

    optimal execution strategy; market impact; transaction cost; stochastic liquidity; limit order book; price manipulation; mean-variance optimization;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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