AI 中文总结
本研究针对价格受限市场，提出含保留隐藏超额收益的随机潜态模型，揭示其产生的记忆效应，分析相关收益率特征并通过模拟与实证验证。
AI 中文摘要
股票的日收益率通常被交易所设定的涨跌幅限制区间所约束，以抑制极端波动，任何试图超出该区间的价格变动都会被截断，留下未被观测的超额收益。我们提出一个最小随机潜态模型，其中部分隐藏超额收益会被保留至次日，这种保留机制即使在每日随机驱动冲击相互独立的情况下也能产生记忆效应。对于具有正则变化尾部的对称驱动冲击，平稳潜态收益率保留了噪声的尾部指数，但尾部振幅增大；在宽区间极限下，当日收益率在任一区间限收市时，可采用单一主导冲击描述。我们表明，此类事件发生后，次日平均收益率符号相同且与区间宽度成比例增长，再次触及同一区间限的概率趋近于有限值；次日触及相反区间限则需要第二个相反符号的极端冲击，且呈幂律被抑制。模拟结果支持这些分析预测，受日涨跌幅限制的股票实证数据与预测的同符号响应及该响应随区间加宽而增大的定性特征一致。
英文摘要
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.
Comments15 pages, 7 figures
