A unified theory of order flow, market impact, and volatility

Battle Count: 72

Extremely relevant to quantitative trading. The paper provides a unified theoretical framework connecting order flow persistence, market impact (square-root law), rough volatility, and trading volume roughness through a single parameter H0. This has direct implications for: (1) execution algorithm design (understanding how order flow impacts prices), (2) market making strategies (reaction flow modeling), (3) volatility forecasting (rough volatility with specific Hurst parameters), (4) trading cost estimation (power-law impact), and (5) understanding the multiscale nature of order flow data. The empirical finding that H0≈3/4 consistently explains multiple stylized facts is particularly valuable for practitioners.

Very high complexity. The paper involves advanced stochastic process theory (Hawkes processes, fractional Brownian motion, mixed fractional processes, scaling limits, Hölder regularity), mathematical finance (no-arbitrage arguments, price impact theory), and statistical estimation (quadratic variations, GMM, autocovariance methods). Implementing the full theoretical framework requires deep expertise in probability theory and stochastic analysis. The empirical estimation procedures are more accessible but still require careful handling of multiscale data and proper specification of the mixed fractional model.

The paper provides complete mathematical proofs in the appendix and detailed estimation procedures. However, the empirical data comes from BMLL Technologies (proprietary trade-by-trade data), which limits full reproducibility. The stock universe (40 stocks) and time period (2021-2024) are specified. The theoretical framework is fully self-contained with all assumptions stated explicitly.