Optimal Execution with Passive Market Impact

Battle Count: 55

Highly relevant to quantitative trading. The paper directly addresses optimal execution with passive orders, a core problem in algorithmic trading. It provides explicit analytical solutions for optimal quote depth, empirical calibration for both equities and FX, and practical insights into the trade-off between fill intensity and passive impact. The mesoscopic framework is particularly applicable to FX markets where order-book models are less natural. The results on how passive impact drives convexity of liquidation curves and affects optimal quoting strategies are directly actionable for execution algorithm design.

The baseline model (m=k) has an elegant closed-form solution via a triangular linear ODE system (Theorem 3.1), making implementation relatively straightforward. However, the extension with different decay rates (m≠k) requires solving a nonlinear triangular system involving the Lambert W function (Theorem 6.1). The transient impact extension (Theorem 6.3) involves a nonlinear first-order PDE in an additional state variable, significantly increasing complexity. Empirical calibration requires access to LOBSTER or LSEG data and implementing MLOFI regression. Monte Carlo simulation for validation is straightforward given the model structure.

The paper provides detailed mathematical derivations, explicit parameter values (Table 1), and estimation procedures. However, the LOBSTER data and LSEG FX data are proprietary and not publicly available. The MLOFI regression coefficients are sourced from Xu et al. [42]. Monte Carlo simulation parameters are specified but code is not provided. The analytical solutions are fully derivable from the paper.