Retained hidden excess generates memory in price-limited markets

Battle Count: 63

The paper provides a mechanistic understanding of post-limit-close return dynamics that is directly relevant to trading strategies around circuit breaker events. The predicted same-sign next-day response growing with band width, the persistence-reversal asymmetry, and the power-law suppression of reversals offer testable predictions for algorithmic trading. However, the model is primarily a theoretical/statistical physics contribution rather than a practical trading system. The empirical validation on NSE data (2007-2026) with multiple band widths (2%, 5%, 10%, 20%) provides actionable insights for markets with price limits, particularly in emerging markets like India.

The core model is a simple discrete-time recursion (X_{t+1} = epsilon_{t+1} + lambda * L_t) that is straightforward to simulate. The analytical derivations involve regular variation theory, contractive stochastic recursions, and single-big-jump principles, which require advanced probability theory. Empirical validation requires careful data processing of NSE records including band history reconstruction, corporate action adjustments, and multiple exclusion criteria. The theoretical predictions (Eqs. 28, 32, 33) involve convergent series and hypergeometric functions that are computable but require numerical evaluation.

The paper provides detailed analytical derivations, explicit simulation parameters (Student's t with specified degrees of freedom and scale), trajectory lengths (10^10), and data processing criteria. NSE data is publicly available via the nselib Python package. However, the raw processed data is only available upon reasonable request from the author, and some data processing steps (band history reconstruction, corporate action handling) are described but not fully reproducible without the exact code.