Order-Flow Modelling for Liquidity and Quoting in Event Time

This thesis investigates high-frequency order flow dynamics, liquidity measurement, and quoting policy through the lens of modern market microstructure. It develops event-driven models and frameworks that improve both the measurement of liquidity and the design of quoting policy in high-frequency markets.

In the first objective, we define an order flow imbalance (OFI) measure in event time. OFI is a well-established directional indicator for short-horizon returns^[1]. While the relationship between future returns and OFI^[1], as well as the effect of past return dynamics on OFI^[2] is established, we find that a general method to forecast OFI under both calendar-time and event-time representations is lacking in the current literature. Prevailing forecasting approaches for OFI assume calendar-time samples, which makes their use with high-frequency event time data challenging^[2, 3]. We propose a generic forecasting algorithm for OFI which can be used with both calendar-time and event-time models. By modeling the buy and sell event streams as a bivariate Hawkes process, we capture the cross excitation and self excitation effects inherent in order flow. Our method of constructing OFI aggregates order flow in event-time, allowing for high-frequency forecasts of buy-sell imbalance. In order to evaluate comparative forecasts from a family of models, we develop a forecast evaluation framework for OFI that accommodates both calendar-time models, such as Vector Auto Regression (VAR), and event-time models, such as Hawkes processes. Within this framework, we introduce a parsimonious loss function to enable systematic forecast comparison across models. This framework allows for robust short-horizon forecasts of high-frequency OFI, which can be calibrated to market regime.

The second objective extends the methodology to the problem of multi-contract quoting. Many algorithmic trading strategies are predicated on simultaneous quoting across contracts^[4–6]. While simultaneous execution is the desired outcome, market design often constrains multi-contract quoting to sequential execution. As a consequence, when quoting across multiple contracts, the order of execution matters. Empirically, it is established in the current literature that the order of execution controls cost^[1]. Specifically, the difference between the desired or quoted spread and the realized spread, termed as slippage^[7, 8], is associated with the order of execution. We posit that the choice of reference contract anchors the spread. This study compares relevant market information for the price stability of the reference contract under two settings - temporal evolution of order flow, and as a derived estimate from the instantaneous snapshot, or state, represented by the limit order book (LOB). Using multivariate Hawkes processes, we model the order flow to construct a stability indicator for reference contract choice that guides liquidity provision when markets are interlinked. We propose a novel Composite Liquidity Factor (CLF), which measures reference contract stability from the instantaneous order book. This framework employs the methodology developed in the first objective to forecast dependent order flow across multiple contracts to inform quoting decisions. We establish a common benchmark for evaluating quoting performance under liquidity constraints, contrasting relative order flow dynamics with indicators derived from the instantaneous LOB.

The third objective deepens this analysis by examining the stability of the reference price in multi-contract high-frequency quoting. We study how transient order events and noisy updates mitigate reference price reliability, and propose filtration methods to extract more robust signals. The central trade-off is explicit: overly aggressive filtering can delay or attenuate reference updates, thereby increasing slippage, whereas insufficient filtering transmits transient disturbances into quotes. To navigate this trade-off, we develop a diagnostic ladder that evaluates candidate filters on transparent criteria - stability, computational efficiency, alignment with event-time order-flow pressure, and execution impact. We then identify conditions under which filtration improves reference stability and enhances the effectiveness of quoting strategies. We contrast the efficacy of OFI by using the diagnostic ladder on two formulations. The first uses all order flow events under filtration to construct OFI, which we term Order Book Imbalance (OBI). The second uses only trade events, as developed in the first objective, to construct the OFI, which is the OBI filtered for trade events. The diagnostic ladder then measures the association of these indicators with returns under multiple conditions. Our empirical results show, that while filtration improves the association between return and OFI, under filtration the association of OBI with returns, shows no significant improvement.

Together, these contributions propose a methodology for modeling and evaluation of OFI forecasts, multi-contract quoting policy dynamics under liquidity constraints and the effect of order-flow filtration on OFI stability. Parsimonious frameworks are developed as a methodological contribution in each objective, allowing for their integration into practical applications. Empirical analyses with high-frequency data sets are used to illustrate the application of the proposed models and methodology.