Multi-Level Order-Flow Imbalance in a Limit Order Book
Multi-Level Order-Flow Imbalance in a Limit Order Book
This paper extends the concept of order-flow imbalance (OFI) to multiple price levels in a limit order book, introducing multi-level order-flow imbalance (MLOFI). Using high-frequency data for six liquid Nasdaq stocks from 2016, the authors fit linear relationships between MLOFI and contemporaneous mid-price changes. While ordinary least squares (OLS) regression reveals strong significance for single-level OFI, it fails to detect significant contributions from deeper levels due to high correlations among MLOFI components. To address this, Ridge regression is employed, which uncovers statistically significant parameters for all price levels up to depth 10. The out-of-sample goodness-of-fit improves substantially with additional levels: 65–75% reduction in RMSE for large-tick stocks and 15–30% for small-tick stocks. These results challenge the earlier conclusion by Cont et al. (2014) that order flow beyond the best quotes has little impact on price changes, highlighting the importance of multi-level order flow in price formation.
Highlights
- 1Introduces multi-level order-flow imbalance (MLOFI), a vector measure of net order flow at multiple price levels in a limit order book.
- 2Demonstrates that including deeper price levels improves out-of-sample goodness-of-fit for mid-price change predictions, contrary to prior findings.
- 3Uses Ridge regression to address multicollinearity in MLOFI components, revealing significant contributions from deeper levels.
- 4Reports 65–75% improvement in out-of-sample RMSE for large-tick stocks and 15–30% for small-tick stocks when using MLOFI over single-level OFI.
Methods
- MMulti-level order-flow imbalance (MLOFI) construction from limit order book event data.
- MOrdinary least squares (OLS) regression for initial linear relationship fitting.
- MRidge regression to handle multicollinearity among MLOFI components.
- MOut-of-sample evaluation using R-squared and root mean squared error (RMSE).
Results
- ROLS regression shows strong significance for single-level OFI but weak significance for deeper levels due to multicollinearity.
- RRidge regression reveals statistically significant parameters for all MLOFI components, including deep price levels.
- RIncluding up to 10 price levels improves out-of-sample RMSE by 65–75% for large-tick stocks and 15–30% for small-tick stocks.
- ROLS overfits for some stocks, while Ridge regression provides more stable out-of-sample performance.
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