[Paper Review] Static vs Adaptive Strategies for Optimal Execution with Signals

Claudio Bellani, Damiano Brigo+2 more|arXiv (Cornell University)|Nov 27, 2018

Auction Theory and ApplicationsDecision Sciences16 references3 citations

TL;DR

This paper demonstrates that adaptive execution strategies significantly reduce transaction costs compared to static strategies in optimal trade execution when incorporating short-term price signals. Using a model with transient market impact and predictive signals, the authors show that updating strategies at intermediate times leads to substantial cost reductions, with Monte Carlo simulations confirming improved performance as update frequency increases.

ABSTRACT

We compare optimal static and dynamic solutions in trade execution. An optimal trade execution problem is considered where a trader is looking at a short-term price predictive signal while trading. When the trader creates an instantaneous market impact, it is shown that transaction costs of optimal adaptive strategies are substantially lower than the corresponding costs of the optimal static strategy. In the same spirit, in the case of transient impact it is shown that strategies that observe the signal a finite number of times can dramatically reduce the transaction costs and improve the performance of the optimal static strategy.

Motivation & Objective

• To investigate whether adaptive strategies offer meaningful cost advantages over static strategies in optimal execution under realistic market conditions.
• To compare static and adaptive execution strategies within a model that incorporates short-term price predictive signals and transient market impact.
• To determine if the improvement in performance from dynamic strategies is quantitatively significant when using realistic parameter values.
• To provide a concrete framework where adaptive strategies outperform static ones, addressing a gap in prior literature where improvements were negligible.

Proposed method

• The authors use a dynamic trading framework from Lehalle and Neumann (2017) that models transient market impact and incorporates a predictive signal for short-term price movements.
• They define a static optimal strategy $X^*$ as a deterministic function of initial signal, inventory, and time horizon, derived from a risk-cost functional.
• They propose a class of adaptive strategies $\widetilde{X}^{(n)}$ that re-optimize at $n-1$ intermediate times $t_k = kT/n$, using updated signal and inventory information.
• The strategy $\widetilde{X}^{(n)}$ is constructed recursively: at each $t_k$, the trader re-computes the optimal liquidation path from $t_k$ to $T$ based on current signal $I_{t_k}$ and remaining inventory.
• Monte Carlo simulations are used to evaluate the expected revenue functional (a proxy for cost reduction) under $\widetilde{X}^{(n)}$ for $n=1,2,3$, comparing performance across update frequencies.
• The model parameters include $\gamma=0.1$, $\sigma=0.1$, $I_0=0.2$, $T=10$, $\rho=1$, $\kappa=0.5$, $X_0=10$, $P_0=10$, with transient impact decaying exponentially.

Experimental results

Research questions

• RQ1 Does the use of adaptive strategies lead to a significant reduction in transaction costs compared to static strategies in a realistic optimal execution model?
• RQ2 How does the frequency of strategy updates based on new signal information affect execution performance in the presence of transient market impact?
• RQ3 Can a model incorporating predictive signals and transient impact yield a non-negligible improvement in cost performance when switching from static to adaptive strategies?
• RQ4 Under what conditions does the dynamic solution outperform the static solution, and is this improvement robust to realistic parameter values?

Key findings

• Adaptive strategies that update at intermediate times reduce transaction costs substantially compared to the optimal static strategy, even with only two updates.
• Monte Carlo simulations show a clear and consistent increase in expected revenue (i.e., cost reduction) as the number of strategy updates increases from $n=1$ to $n=3$.
• The improvement is not trivial: the dynamic strategy $\widetilde{X}^{(2)}$ exhibits a distinct jump at $t=5$, reflecting the impact of updated signal information on execution path.
• The performance gain is observed even with realistic parameter values, resolving a gap in prior literature where improvements were negligible under similar models.
• The results confirm that the class of adaptive strategies significantly outperforms static strategies in models that incorporate both predictive signals and transient market impact.