On a Simple Relationship Between Order Imbalance, Skew and Width in Over-The-Counter Trading

Battle Count: 64

Highly relevant to quantitative trading, particularly for OTC market making, RFQ-based execution, and dealer inventory management. The paper provides exact, parameter-free formulas for how flow imbalance should affect quoting (skew and width), directly applicable to algorithmic market-making systems. The CWLS benchmark analysis clarifies when common heuristics are valid and when they fail. The fill-ratio diagnostic and post-trade attribution framework are practically useful. The symmetry reduces the dimensionality of the policy space, which is valuable for both analytical and ML-based market-making systems. However, it is a theoretical paper with no empirical validation, and the general solution still requires numerical computation.

The symmetry correction itself is trivial to implement: given a balanced solution, apply three explicit transformations (translate skew by δ, widen by γ, multiply carry cost by M(q)). The observable width w and imbalance q are directly estimable from market data. However, the underlying balanced solution ν(x) generally requires numerical computation of the consistency equation (3), and the shape depends on the full cost-of-carry function c(x). The constant-width special case (Section 4) is more tractable with the closed-form skew formula (7). The local exponentiality check requires a numerical script. Overall, the correction is simple but the base solution is not.

The paper provides a complete analytical derivation with explicit formulas. A verification script (verify_local_exponentiality.py) accompanies the paper to check the local exponentiality assumption numerically. The model is fully specified with clear assumptions (Poisson arrivals, exponential competing quotes, fixed trade size). However, the general solution for ν(x) requires numerical computation, and no empirical dataset is provided for validation. The companion paper with Papanicolaou extends the model.