Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Strategic Execution Trajectories

Strategic Execution Trajectories We obtain the optimal execution strategy for two sequential trades in the presence of a transient price impact. We first present a novel and general solution method for the case of a single trade (a metaorder) that is executed as a sequence of sub-trades (child orders). We then analyze the case of two sequential metaorders, including the case where the size and direction of the second metaorder are uncertain at the time the first metaorder is initiated. We obtain the optimal execution strategy under two different cost functions. First, we minimize the total cost when each metaorder is benchmarked to the price at its initiation, the total separate costs approach widely used by practitioners. Although simple, we show that optimizing total separate costs can lead to a significant understatement of the real costs of trading whilst also adversely impacting order scheduling. We overcome these issues by introducing a new cost function that splits the second metaorder into two parts, one that is predictable when the first metaorder is initiated and a residual that is not. The predictable and residual parts of the second metaorder are benchmarked using the initiation prices of the first and second metaorders, respectively. We prove existence of an optimal execution trajectory for linear instantaneous price impact and positive definite decay, and derive the explicit form of the minimizer in the special case of exponentially decaying impact, however uniqueness in general remains unproven. Various numerical examples are included for illustration. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematical Finance Taylor & Francis

Strategic Execution Trajectories

Download PDF
43 pages

Loading next page...
 
/lp/taylor-francis/strategic-execution-trajectories-A8tDYxSrkV

References

References for this paper are not available at this time. We will be adding them shortly, thank you for your patience.

Publisher
Taylor & Francis
Copyright
© 2023 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group
ISSN
1466-4313
eISSN
1350-486X
DOI
10.1080/1350486X.2023.2194658
Publisher site
See Article on Publisher Site

Abstract

We obtain the optimal execution strategy for two sequential trades in the presence of a transient price impact. We first present a novel and general solution method for the case of a single trade (a metaorder) that is executed as a sequence of sub-trades (child orders). We then analyze the case of two sequential metaorders, including the case where the size and direction of the second metaorder are uncertain at the time the first metaorder is initiated. We obtain the optimal execution strategy under two different cost functions. First, we minimize the total cost when each metaorder is benchmarked to the price at its initiation, the total separate costs approach widely used by practitioners. Although simple, we show that optimizing total separate costs can lead to a significant understatement of the real costs of trading whilst also adversely impacting order scheduling. We overcome these issues by introducing a new cost function that splits the second metaorder into two parts, one that is predictable when the first metaorder is initiated and a residual that is not. The predictable and residual parts of the second metaorder are benchmarked using the initiation prices of the first and second metaorders, respectively. We prove existence of an optimal execution trajectory for linear instantaneous price impact and positive definite decay, and derive the explicit form of the minimizer in the special case of exponentially decaying impact, however uniqueness in general remains unproven. Various numerical examples are included for illustration.

Journal

Applied Mathematical Finance – Taylor & Francis

Published: Jul 4, 2022

Keywords: Market impact; optimal transport; optimal trade execution; transactions costs; variational analysis

References

  • Optimal Execution Strategies in Limit Order Books with General Shape Functions
  • Optimal Execution of Portfolio Transactions
  • Direct Estimation of Equity Market Impact
  • The Non-Linear Market Impact of Large Trades: Evidence From Buy-Side Order Flow
  • Cumulative Market Impact of Consecutive Orders Over One and Two Days: How Long Does the Market Remember Past Trades?
  • From Bachelier to Dupire Via Optimal Transport
  • Fluctuations and Response in Financial Markets: The Subtle Nature of ‘random’ Price Changes
  • Random Walks, Liquidity Molasses and Critical Response in Financial Markets
  • Slow Decay of Impact in Equity Markets: Insights From the ANcerno Database
  • A Closed-Form Execution Strategy to Target Volume Weighted Average Price
  • Optimal Execution with Nonlinear Transient Market Impact
  • Martingale Optimal Transport and Robust Hedging in Continuous Time
  • Robust Hedging with Proportional Transaction Costs
  • A Fully Consistent, Minimal Model for Non-Linear Market Impact
  • Optimal Trade Execution for Gaussian Signals With Power-Law Resilience
  • Optimal Execution of a VWAP Order: A Stochastic Control Approach
  • A Survey of Some Recent Applications of Optimal Transport Methods to Econometrics
  • No Dynamic Arbitrage and Market Impact
  • Transient Linear Price Impact and Fredholm Integral Equations
  • Quantifying Long-Term Market Impact
  • Price Manipulation and Quasiarbitrage
  • Option Pricing with Linear Market Impact and Nonlinear Black-Scholes Equations
  • Optimal Trading Strategy and Supply/Demand Dynamics
  • The Implementation Shortfall: Paper Versus Reality
  • Optimal Execution in a General One-Sided Limit-Order Book
  • Choosing Benchmarks Vs. Choosing Strategies: Part 1-Execution Benchmarks: VWAP or Pretrade Prices