Optimal Trading Filters and the Value of Predictive Signals

By Matteo Smerlak

Rating

1787
Battle Count: 52

Relevance

9/10
Highly relevant for practitioners dealing with high-frequency or mid-frequency trading where transient price impact and signal predictability are critical. Provides explicit formulas for optimal execution and signal valuation.

Implementation Complexity

8/10
High complexity due to the use of Wiener-Hopf factorization and fractional calculus for power-law impact. Requires advanced mathematical understanding to implement the causal filters correctly, especially for non-rational transfer functions.

Reproducibility

3/5
The paper provides full analytical derivations and explicit formulas for the optimal policies and values under specified assumptions (Gaussian predictors, specific impact kernels). No code repository is provided, but the mathematical framework is fully described, allowing for independent implementation of the theoretical results.

Abstract

The value of a forecast depends on its accuracy, but also on its actionability. In trading, an investor must translate return forecasts into positions while accounting for trading costs and the lingering impact of earlier trades. We solve the stationary quadratic trading problem with transient price impact using tools from prediction theory: Wiener-Hopf factorization gives the optimal policy as the composition of a conditional forecast and an explicit causal linear filter. We recover the Gârleanu-Pedersen aim-portfolio under exponential resilience and derive fractional trading filters under power-law impact decay, requiring memory beyond finite-dimensional LQR control. At fixed positive risk penalty, signals of equal instantaneous predictive strength have equal frictionless Markowitz value. With trading costs, net attainable value is determined by the mean square of the friction-weighted conditional forecast. Under power-law impact with exposure bleeding, we find an intermediate optimal mean-reversion rate for Ornstein-Uhlenbeck signals.

Links

arXiv:2610.24558 · Paper rankings

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