Marked point processes and intensity ratios for limit order book modeling

This paper extends the analysis of Muni Toke and Yoshida (2020) to the case of marked point processes. We consider multiple marked point processes with intensities defined by three multiplicative components, namely a common baseline intensity, a state-dependent component specific to each process, and a state-dependent component specific to each mark within each process. We show that for specific mark distributions, this model is a combination of the ratio models defined in Muni Toke and Yoshida (2020). We prove convergence results for the quasi-maximum and quasi-Bayesian likelihood estimators of this model and provide numerical illustrations of the asymptotic variances. We use these ratio processes to model transactions occurring in a limit order book. Model flexibility allows us to investigate both state-dependency (emphasizing the role of imbalance and spread as significant signals) and clustering. Calibration, model selection and prediction results are reported for high-frequency trading data on multiple stocks traded on Euronext Paris. We show that the marked ratio model outperforms other intensity-based methods (such as “pure” Hawkes-based methods) in predicting the sign and aggressiveness of market orders on financial markets.

Volatility and Depth in Commodity and FX Futures Markets

Prior theory suggests a positive relation between volatility and market depth, while past empirical research finds contrasting results. This paper examines the relation between the volatility and the limit order book depth in commodity and foreign exchange futures markets during a turbulent time using the generalized method of moments (GMM). Results indicate a negative relation between volatility and depth and suggest that the depth in the limit order book decreases as volatility increases. Findings help to understand how market participants provide liquidity in response to shifts in prices.

The Relation between Intraday Limit Order Book Depth and Spread

Prior studies that examine the relation between market depth and bid–ask spread are often limited to the first level of the limit order book. However, the full limit order book provides important information beyond the first level about the depth and spread, which affects the trading decisions of market participants. This paper examines the intraday behavior of depth and spread in the five-deep limit order book and the relation between depth and spread in a futures market setting. A dummy-variables regression framework is employed and is estimated using the generalized method of moments (GMM). Results indicate an inverse U-shaped pattern for depth and an increasing pattern for spread. After controlling for known explanatory factors, an inverse relation between the limit order book depth and spread is documented. The inverse relation holds for depth and spread at individual levels in the limit order book as well. Results indicate that market participants actively manage both the price (spread) and quantity (depth) dimensions of liquidity along the five-deep limit order book.