Retained hidden excess generates memory in price-limited markets

2026-08-09

AI Summary

This study addresses the challenge posed by price limits on daily stock returns, which truncate extreme movements and generate unobservable “hidden excesses” that impede modeling of market memory effects. The authors propose the first minimal stochastic hidden-state model that formalizes the carryover mechanism of these hidden excesses across consecutive days as a source of endogenous memory. Under independent exogenous shocks, the model successfully reproduces persistent return responses. Through rigorous analysis involving stochastic processes, hidden-state dynamics, and heavy-tailed distributions—augmented by a single-dominant-shock limiting approximation—the framework theoretically predicts that same-direction next-day average returns scale linearly with the price limit magnitude, the probability of repeated same-side limit hits converges to a constant, and opposite-direction breakouts are suppressed by a power law. Simulations and empirical evidence qualitatively corroborate these predictions, demonstrating that endogenous memory can emerge even when underlying shocks are independent.

Abstract

The daily return of a stock is often restricted to an exchange-imposed band to curb extreme fluctuations. Any attempted price movement beyond this band is clipped, leaving an unobserved excess. We introduce a minimal stochastic latent-state model in which a fraction of this hidden excess is retained for the next day. This retention generates memory, even though the daily stochastic driving shocks are independent. For symmetric driving shocks with regularly varying tails, the stationary latent return preserves the tail index of the noise, but has an enhanced tail amplitude. In the wide-band limit, a close of the daily return at either limit of the band admits a single-dominant-shock description. We show that after such an event, the mean return on the following day has the same sign and grows proportionally to the band width, while the probability of reaching the same limit again approaches a finite value. Reaching the opposite band limit on the following day requires a second extreme shock of opposite sign and is power-law suppressed. Simulations support these analytical predictions. Empirical data from stocks subject to daily price limits are qualitatively consistent with the predicted same-sign response and its increase across wider price bands.

Problem

• price limits
• hidden excess
• market memory
• latent returns
• extreme shocks

Innovation

• price limits
• hidden excess
• memory effect
• latent-state model
• tail behavior