Order book curvature as a liquidity measure: evidence on high- frequency volatility in crude oil futures

Abstract

This thesis proposes the limit order book (LOB) curvature as a new measure of liquidity. Using high-frequency data on crude oil futures traded on the CME, curvature is estimated from a power-law relation between normalized cumulative price distance and normalized cumulative depth, capturing how liquidity is distributed across the order book. This thesis uses a vector autoregression (VAR) model with impulse-response functions, examining the dynamic links among curvature, depth, spreads, and returns, while two-scale realized volatility (TSRV) is used to assess its predictive power for short-term volatility. Results show that curvature shocks reduce depth, widen spreads, and that curvature significantly improves volatility forecasts beyond traditional liquidity measures. The effect of scheduled news such as U.S. Energy Information Administration (EIA) Weekly Petroleum Status Report is insignificant after controlling the intraday seasonality, implying that liquidity dynamics are largely endogenous and resilient, with structural adjustments restoring equilibrium after transient imbalances rather than reacting to new information. Overall, curvature provides a unified non-linear perspective for understanding liquidity dynamics and volatility in high-frequency futures markets, offering new insight for market microstructure research and practice.