Optimal Size in Market Making under State-Dependent Hawkes Process

Abstract

We study market making with a parametric model of executed volume that accounts for quote placement and state-dependent order flow. Executed volume is expressed as the product of an average order size, an exponential demand function, and a Prony-series multiplier depending on quote depth, market-order count constructed from a state-dependent Hawkes model. An approximation result for finite Prony sums on a compact state domain provides a mathematical basis for the representation. An empirical study of limit-order-book data examines the calibrated demand and intensity models, sensitivity to inventory restrictions, and the resulting placement policies. In retrospective evaluations conditional on realised order-flow paths, the selected calibration achieves higher terminal utility than a baseline while respecting the prescribed inventory bound. The comparisons also distinguish the contribution of trading revenues from that of inventory control. The resulting closed-form volume specification takes placement levels as inputs and can therefore be used with alternative quoting rules.