Optimal Size in Market Making under State-Dependent Hawkes Process
Chávez Casillas and Gan
A closed-form model of executed volume, combining an exponential demand function with a Prony-series multiplier driven by a state-dependent Hawkes process, is calibrated to limit-order-book data for market making.
Source published · In the Daily Brief of 27 October 2026
Filed under Market microstructure, Quantitative finance
The paper models the volume a market maker executes as the product of an average order size, an exponential demand function of quote depth, and a Prony-series multiplier that depends on depth and on market-order counts generated by a state-dependent Hawkes process. An approximation result for finite Prony sums on a compact state domain justifies the representation.
Calibrated on limit-order-book data, the chosen specification earns higher terminal utility than a baseline in retrospective tests conditional on realised order flow, while respecting an inventory bound. Because placement levels are inputs, the volume formula can be combined with other quoting rules.