Paper: arXiv 2604.20406

Authors: Alexander Barzykin, Axel Ciceri

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 á 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.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous theoretical framework using stochastic optimal control, Hamilton-Jacobi-Bellman (HJB) equations, and Riccati approximations to model market making with hit-ratio targets. However, as described in the summary, it is primarily a theoretical and methodological contribution with little to no empirical backtesting or real market data validation.

Research Flowchart

  flowchart TD
    A["Research Goal: Optimal OTC Bond Market Making<br>with Hit-Ratio Target & Size Ladder"] --> B["Inputs: Inventory Risk, Client Tiers,<br>Fill Probabilities & Target Hit Ratio"]
    B --> C["Formulate Stochastic Optimal Control &<br>Dualize Hit-Ratio Constraint in HJB Equation"]
    C --> D["Apply Quadratic Approximation<br>(Bergault et al.) to Derive Riccati System"]
    D --> E["Linearize Riccati System for<br>Explicit Analytical Quotes"]
    E --> F["Outcomes: Exact Quote Decompositions into<br>Riskless Spread, Inventory & Hit-Ratio Corrections"]