Bond Market Making with a Hit-Ratio Target

Battle Count: 81

Highly relevant to quantitative trading, particularly in the domain of OTC bond market making and RFQ-based execution. The paper directly addresses how dealers should optimally quote when balancing profitability, inventory risk, and hit-ratio targets—a central practical problem in electronic bond dealing. The explicit quote decomposition (riskless spread + inventory correction + hit-ratio correction) is directly implementable in trading systems. The multi-bond, multi-tier generalization covers realistic desk configurations. The BEGV-style approximations provide computationally tractable solutions suitable for production systems.

The theoretical framework involves solving matrix Riccati equations, Hamiltonian optimization, and dual variable closures. The exact solution requires numerical HJB solving (explicit Euler scheme). The BEGV quadratic approximation reduces complexity significantly, yielding closed-form Riccati solutions and explicit quote formulas. The linearized form provides the simplest implementation with three-component quote decomposition. However, handling multi-bond covariance matrices, multiple client tiers, size ladders, and the implicit fixed-point for dual variables adds practical complexity. The JAX-based numerical implementation with Hamiltonian interpolators requires careful engineering.

The paper provides detailed mathematical formulations, parameter settings for numerical examples (size ladder z=(1,5,20)M, RFQ intensities λ_z=(500,200,50) day⁻¹, sigmoid win probability parameters, target hit ratio r*=0.1, inventory penalty φ=1, horizon T=1 day, q_max=100M, η=0), and describes the numerical scheme (explicit Euler in JAX with pre-calculated Hamiltonian interpolators). However, no code repository is provided, and the numerical implementation details (JAX code, interpolator construction) are not fully specified. The theoretical derivations are self-contained and reproducible analytically.