Bond Market Making with a Hit-Ratio Target

TL;DR

This paper develops a stochastic optimal control model for OTC bond market making that targets a specific hit ratio, providing explicit optimal controls and a quadratic approximation for practical implementation.

Contribution

It introduces a novel control framework for bond market making with a hit ratio target, deriving explicit solutions and a quadratic approximation for complex multi-bond scenarios.

Findings

Exact optimal controls derived via Hamilton-Jacobi-Bellman equation

Quadratic approximation yields explicit quote decompositions

Model applicable to multi-bond, multi-client-tier scenarios

Abstract

We study OTC bond market making on a size ladder with quadratic inventory penalty and a running target on the dealer's size-weighted hit ratio within a stochastic optimal control approach. We demonstrate that the corresponding reduced Hamilton-Jacobi-Bellman (HJB) equation remains separable by dualizing the hit ratio target term and provides the exact optimal controls through the inverse of the fill-probability function and the Hamiltonian derivative. We then focus on the quadratic approximation \'a la Bergault et al., which yields a Riccati equation for the inventory curvature while retaining the exact quote map. In its linearized form, this approximation produces explicit quote decompositions into riskless spread, inventory-risk correction, and hit-ratio correction. The formulation is general and applies to multi-bond, multi-client-tier scenarios, with special cases obtained by restricting the targeted tiers, their bond coverage, and their associated targets.