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arxiv: 2605.30643 · v1 · pith:WFRTU4TCnew · submitted 2026-05-28 · 💱 q-fin.TR · q-fin.RM

Quality-Adjusted Hit-Ratio Targeting in Corporate Bond Market Making

Bouna Niang This is my paper

Pith reviewed 2026-06-28 23:19 UTC · model grok-4.3

classification 💱 q-fin.TR q-fin.RM
keywords corporate bond market makinghit ratioadverse selectionstochastic controlRFQ quotinginventory managementquality adjustmentresidual toxicity
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The pith

Replacing raw hit-ratio targets with a residual-quality-adjusted version reallocates corporate bond market-making service away from high-toxicity client flow.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Raw hit-ratio targets in corporate bond RFQ market making treat all client flow equally, which can subsidize orders that produce large unexplained losses after observable factors are stripped out. The paper replaces the raw constraint with a quality-adjusted version that decomposes adverse post-trade markouts into credit factors, carry and rolldown, issuer relative value, index or ETF demand effects, and a residual adverse-selection component; only the residual enters the penalty. The resulting stochastic-control problem stays tractable because dualizing the quality-hit-ratio term keeps the Hamilton-Jacobi-Bellman equation separable, with the dual variable recovered from a one-dimensional nonlinear fixed-point equation per tier. Quadratic value-function approximation then yields explicit optimal quotes that add a residual-toxicity charge and a quality-hit-ratio subsidy to the usual riskless spread and inventory skew. Synthetic multi-bond simulations confirm that the adjusted target shifts service toward low-residual-toxicity flow and raises the attainable service-versus-economics frontier relative to raw hit-ratio targeting.

Core claim

The central claim is that a residual-quality-adjusted hit ratio, formed by first removing observable credit, carry, relative-value, and demand effects from post-trade markouts and penalizing only the remaining adverse-selection component, produces a tractable control problem whose solution reallocates quoting service away from residual-toxic flow. Under the quadratic approximation the optimal quote decomposes into riskless spread, inventory skew, credit-alpha skew, residual-toxicity charge, and quality-hit-ratio subsidy; the dual variable for each targeted tier solves an exact one-dimensional nonlinear fixed point. Multi-bond simulations with nonlinear dual solves show that raw hit-ratio con

What carries the argument

Residual-quality-adjusted hit ratio obtained by decomposing adverse markouts into observable factors and penalizing only the residual adverse-selection component inside the stochastic-control penalty.

If this is right

  • Optimal quotes explicitly include a residual-toxicity charge and a quality-hit-ratio subsidy in addition to riskless spread, inventory skew, and credit-alpha skew.
  • Raw hit-ratio targets can subsidize residual-toxic flow while quality-adjusted targets reallocate service toward low-residual-toxicity clients.
  • The dual variable for each hit-ratio tier solves a one-dimensional nonlinear fixed-point equation, keeping the HJB separable.
  • Inventory-recycling value through risk-aware style-aligned warehousing of sweep or portfolio trades can be sized with the same quadratic approximation used for RFQ quoting.
  • Forecastable passive or index-demand flow is handled as a special case of the same control problem.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The decomposition approach could be tested on other OTC asset classes where post-trade markouts contain both observable and residual components.
  • Relaxing the quadratic value-function approximation would allow direct numerical solution of the HJB to quantify approximation error in the optimal quotes.
  • Portfolio-trade participation rules derived from the warehousing extension could interact with the quality-adjusted hit-ratio constraint when multiple bonds are quoted simultaneously.
  • If the residual component proves stable across market regimes, the same fixed-point dual solve could be embedded in real-time quoting engines without proprietary data.

Load-bearing premise

Adverse post-trade markouts can be decomposed accurately enough that the leftover residual component truly isolates client-flow toxicity rather than omitted observable effects.

What would settle it

Live RFQ data in which the residual component after the stated decomposition shows no out-of-sample predictive power for subsequent adverse markouts, or in which the quality-adjusted quotes fail to improve realized profitability per unit of hit ratio relative to raw targeting.

Figures

Figures reproduced from arXiv: 2605.30643 by Bouna Niang.

Figure 1
Figure 1. Figure 1: Nonlinear-dual attained service/economics frontier. The x-axis is realized residual-quality [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Interpolated PnL saving of residual-quality targeting over raw targeting at matched [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Cost of raw hit ratio at the 8% target. Residual-quality targeting gives up some spread [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Flow allocation by policy at the 8% target. Residual-quality targeting reallocates wins [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Mean PnL versus terminal inventory risk at the 8% target. [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Liquidation-cost sensitivity of the residual-quality PnL saving across target levels. [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Style-aware client-flow warehousing with random Sweep fills. The risk-aware rule im [PITH_FULL_IMAGE:figures/full_fig_p016_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Matched-quality comparison for style-aware client-flow warehousing. The risk-aware rule [PITH_FULL_IMAGE:figures/full_fig_p017_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Synthetic passive/index event profile used in the reduced-form extension. [PITH_FULL_IMAGE:figures/full_fig_p020_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: TW Sweep scenario grid at an 8% target. Cells report mean PnL per day. [PITH_FULL_IMAGE:figures/full_fig_p021_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Best TW Sweep fraction in the reduced-form grid. Forecast quality, not raw passive [PITH_FULL_IMAGE:figures/full_fig_p021_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Baseline one-bond ask quote offset as a function of inventory. The figure checks the [PITH_FULL_IMAGE:figures/full_fig_p022_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Baseline one-bond hit ratio as a function of inventory. The hit-ratio target interacts [PITH_FULL_IMAGE:figures/full_fig_p023_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Baseline one-bond dual variable as a function of inventory. The nonlinearity of the dual [PITH_FULL_IMAGE:figures/full_fig_p023_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Synthetic markout decomposition used to motivate residual toxicity. Two flows can have [PITH_FULL_IMAGE:figures/full_fig_p024_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Top-of-book quote offsets at zero inventory under raw targeting, naive gross-markout [PITH_FULL_IMAGE:figures/full_fig_p024_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Segment hit ratios under the clean residual-toxicity policy as inventory varies. The [PITH_FULL_IMAGE:figures/full_fig_p025_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Forward-Kolmogorov hit-ratio comparison in the one-bond residual-toxicity example. [PITH_FULL_IMAGE:figures/full_fig_p025_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Forward-Kolmogorov residual economics in the one-bond example. The clean residual [PITH_FULL_IMAGE:figures/full_fig_p026_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: Raw hit ratio versus residual-quality hit ratio across policies in the multi-bond synthetic [PITH_FULL_IMAGE:figures/full_fig_p026_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: Segment hit ratios in the multi-bond simulation. Raw hit-ratio targeting wins residual [PITH_FULL_IMAGE:figures/full_fig_p027_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: Cross-inventory quote skew in a credit-factor book. A long position in one bond widens [PITH_FULL_IMAGE:figures/full_fig_p027_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: Mean PnL versus residual-toxic hit ratio in the multi-bond simulation. Policies that [PITH_FULL_IMAGE:figures/full_fig_p028_23.png] view at source ↗
Figure 24
Figure 24. Figure 24: Target frontier from the multi-bond simulation before interpolation by attained residual [PITH_FULL_IMAGE:figures/full_fig_p028_24.png] view at source ↗
Figure 25
Figure 25. Figure 25: PnL saving from residual-quality targeting over raw targeting by hit-ratio target in the [PITH_FULL_IMAGE:figures/full_fig_p029_25.png] view at source ↗
Figure 26
Figure 26. Figure 26: Service reallocation by target: residual-quality targeting reduces residual-toxic hit ratio [PITH_FULL_IMAGE:figures/full_fig_p029_26.png] view at source ↗
Figure 27
Figure 27. Figure 27: Robustness heatmap: PnL saving as a function of quality-weight strength [PITH_FULL_IMAGE:figures/full_fig_p030_27.png] view at source ↗
Figure 28
Figure 28. Figure 28: Robustness heatmap: residual-toxic hit-ratio reduction as a function of [PITH_FULL_IMAGE:figures/full_fig_p030_28.png] view at source ↗
Figure 29
Figure 29. Figure 29: Robustness heatmap: PnL saving as a function of residual-toxicity scale and credit-alpha [PITH_FULL_IMAGE:figures/full_fig_p031_29.png] view at source ↗
Figure 30
Figure 30. Figure 30: Exact scalar dual variable versus the local linearized dual approximation. The compar [PITH_FULL_IMAGE:figures/full_fig_p031_30.png] view at source ↗
Figure 31
Figure 31. Figure 31: Error of the linearized dual approximation versus inventory stress. Approximation errors [PITH_FULL_IMAGE:figures/full_fig_p032_31.png] view at source ↗
Figure 32
Figure 32. Figure 32: Passive/index extension frontier by forecast skill with a fixed 50 percent sweep pre [PITH_FULL_IMAGE:figures/full_fig_p032_32.png] view at source ↗
Figure 33
Figure 33. Figure 33: Passive/index versus residual-toxic hit ratios at the 8 percent target. The extension [PITH_FULL_IMAGE:figures/full_fig_p033_33.png] view at source ↗
Figure 34
Figure 34. Figure 34: PnL decomposition for the passive/index extension. Forecastable index flow adds recy [PITH_FULL_IMAGE:figures/full_fig_p033_34.png] view at source ↗
Figure 35
Figure 35. Figure 35: TW Sweep pre-positioning PnL distribution at the 8 percent target across selected [PITH_FULL_IMAGE:figures/full_fig_p034_35.png] view at source ↗
Figure 36
Figure 36. Figure 36: Small-sample nonlinear-dual frontier used as an implementation check before the larger [PITH_FULL_IMAGE:figures/full_fig_p034_36.png] view at source ↗
Figure 37
Figure 37. Figure 37: Small-sample nonlinear-dual PnL-saving check. The main text reports the larger [PITH_FULL_IMAGE:figures/full_fig_p035_37.png] view at source ↗
Figure 38
Figure 38. Figure 38: Small-sample nonlinear-dual toxic-flow reduction check. The main text reports the [PITH_FULL_IMAGE:figures/full_fig_p035_38.png] view at source ↗
Figure 39
Figure 39. Figure 39: Risk-aware style-flow PnL attribution relative to the residual-quality baseline. The [PITH_FULL_IMAGE:figures/full_fig_p036_39.png] view at source ↗
Figure 40
Figure 40. Figure 40: Style-alpha exposure and PnL at the 8 percent target. Risk-aware participation improves [PITH_FULL_IMAGE:figures/full_fig_p036_40.png] view at source ↗
Figure 41
Figure 41. Figure 41: Franchise-quality sensitivity. The probability that client inventory is style-aligned affects [PITH_FULL_IMAGE:figures/full_fig_p037_41.png] view at source ↗
read the original abstract

Hit ratio is a common service metric for electronic corporate bond market making, but raw hit-ratio targets can be economically misleading when client flow has heterogeneous adverse-selection content. This paper extends a stochastic-control framework for OTC bond RFQ market making with hit-ratio constraints by replacing raw hit ratio with a residual-quality-adjusted hit ratio. The key modelling distinction is that adverse post-trade markouts are first decomposed into observable credit factors, carry/rolldown, issuer-relative-value effects, index or ETF demand effects, and residual adverse selection. Only the residual component is treated as client-flow toxicity. The resulting control problem remains tractable: after dualizing the quality-hit-ratio penalty, the HJB retains separable Hamiltonians, and the dual variable is the solution of an exact one-dimensional nonlinear fixed point for each targeted tier. Under a quadratic value-function approximation, optimal quotes decompose into a riskless spread, inventory skew, credit-alpha skew, residual-toxicity charge, and quality-hit-ratio subsidy. Synthetic multi-bond simulations with nonlinear dual solves illustrate that raw hit-ratio targeting can subsidize residual-toxic flow, while residual-quality targeting reallocates service toward low-residual-toxicity flow and improves the attained service/economics frontier. A final reduced-form extension studies inventory-recycling value through risk-aware style-aligned client-flow warehousing. Sweep or portfolio-trade opportunities fill randomly, and participation is sized using the same quadratic value approximation as the RFQ quoting problem. A passive/index-demand experiment is reported in the appendix as a special case of forecastable client flow. The numerical evidence is synthetic and mechanism-oriented; no proprietary RFQ data are used.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper extends a stochastic-control model for OTC corporate-bond RFQ market making by replacing a raw hit-ratio constraint with a residual-quality-adjusted hit ratio. Adverse post-trade markouts are decomposed into observable components (credit factors, carry/rolldown, issuer RV, index/ETF demand) plus a residual adverse-selection term that alone is treated as client-flow toxicity. After dualization the HJB remains separable; the dual variable solves a one-dimensional nonlinear fixed point per tier. Under a quadratic value-function approximation the optimal quotes decompose into riskless spread, inventory skew, credit-alpha skew, residual-toxicity charge and quality-hit-ratio subsidy. Synthetic multi-bond simulations with nonlinear dual solves are used to illustrate that raw hit-ratio targeting subsidizes residual-toxic flow while the quality-adjusted version reallocates service toward low-residual-toxicity counterparties and improves the service/economics frontier. A reduced-form inventory-recycling extension and a passive/index-demand appendix case are also presented. All evidence is synthetic; no proprietary RFQ data appear.

Significance. If the clean decomposition of markouts into observables versus residual toxicity can be maintained in live trading, the framework supplies a tractable way to enforce service metrics without inadvertently subsidizing toxic flow. The dual fixed-point construction and quadratic approximation preserve separability, which is a technical strength for implementation. However, because the reported frontier improvement is demonstrated only under perfect synthetic decomposition and no real-market validation or perturbation analysis is supplied, the practical significance remains illustrative rather than immediately actionable for market-making desks.

major comments (2)
  1. [Synthetic multi-bond simulations] The central claim that residual-quality targeting 'reallocates service toward low-residual-toxicity flow and improves the attained service/economics frontier' is demonstrated exclusively in synthetic multi-bond simulations where the markout decomposition is exact by construction. No perturbation analysis (noisy factor estimates, omitted variables, or residual contamination) is reported to show whether the HJB-derived quotes or the one-dimensional nonlinear fixed-point dual still deliver the claimed improvement when the residual is imperfectly observed. This assumption is load-bearing for the modeling distinction stated in the abstract.
  2. [Abstract / dualization paragraph] The abstract states that the dual variable 'is the solution of an exact one-dimensional nonlinear fixed point for each targeted tier,' yet the manuscript supplies neither the explicit fixed-point equation nor an error analysis or convergence proof for the nonlinear solve. Without these derivations it is impossible to assess whether the fixed point remains independent of the target result or reduces to a fitted quantity, undermining the claim of tractability after dualization.
minor comments (1)
  1. The quadratic value-function approximation is listed among the free parameters; its functional form and calibration procedure should be stated explicitly in the main text rather than left implicit.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments. The feedback correctly identifies that the current evidence is limited to exact synthetic decompositions and that the dual fixed-point construction requires more explicit derivation. We address each point below and will incorporate the suggested additions in revision.

read point-by-point responses

  1. Referee: [Synthetic multi-bond simulations] The central claim that residual-quality targeting 'reallocates service toward low-residual-toxicity flow and improves the attained service/economics frontier' is demonstrated exclusively in synthetic multi-bond simulations where the markout decomposition is exact by construction. No perturbation analysis (noisy factor estimates, omitted variables, or residual contamination) is reported to show whether the HJB-derived quotes or the one-dimensional nonlinear fixed-point dual still deliver the claimed improvement when the residual is imperfectly observed. This assumption is load-bearing for the modeling distinction stated in the abstract.

    Authors: We agree that the simulations assume exact decomposition by construction, which isolates the mechanism but leaves open the question of robustness. In the revision we will add a new subsection containing perturbation experiments: Gaussian noise will be added to the observable markout components, omitted-variable scenarios will be simulated, and residual contamination will be introduced. The HJB quotes and the nonlinear dual fixed-point solves will be re-computed under these conditions to test whether the reported service/economics frontier improvement is preserved. This directly addresses the load-bearing assumption. revision: yes

  2. Referee: [Abstract / dualization paragraph] The abstract states that the dual variable 'is the solution of an exact one-dimensional nonlinear fixed point for each targeted tier,' yet the manuscript supplies neither the explicit fixed-point equation nor an error analysis or convergence proof for the nonlinear solve. Without these derivations it is impossible to assess whether the fixed point remains independent of the target result or reduces to a fitted quantity, undermining the claim of tractability after dualization.

    Authors: We acknowledge that the explicit fixed-point equation and convergence details are not supplied in the current text. The revision will add an appendix that (i) derives the one-dimensional nonlinear fixed-point equation obtained after dualization of the quality-adjusted hit-ratio constraint, (ii) states the precise mapping from the dual variable to the target tier, and (iii) reports numerical convergence diagnostics (iteration counts and residual norms) for a range of target values. This will allow readers to verify independence from the target and confirm tractability. revision: yes

Circularity Check

1 steps flagged

Synthetic simulations demonstrate reallocation benefit under exact decomposition by construction

specific steps
  1. fitted input called prediction [Abstract]
    "Synthetic multi-bond simulations with nonlinear dual solves illustrate that raw hit-ratio targeting can subsidize residual-toxic flow, while residual-quality targeting reallocates service toward low-residual-toxicity flow and improves the attained service/economics frontier."

    The synthetic data is generated from the same credit factors, carry/rolldown, issuer-relative-value, and index/ETF demand components used to decompose markouts and isolate the residual toxicity term. The claimed improvement therefore obtains by construction whenever the decomposition is exact, without independent falsification.

full rationale

The paper's central claim—that residual-quality-adjusted hit-ratio targeting improves the service/economics frontier relative to raw hit-ratio targeting—is illustrated exclusively via synthetic multi-bond simulations. These simulations generate markout data from the identical observable factors (credit, carry/rolldown, issuer RV, index/ETF demand) used to define the decomposition, with only the residual labeled toxicity. Consequently the reported reallocation and frontier improvement hold exactly when the decomposition is perfect, which is the modeling assumption itself. The HJB separability and one-dimensional dual fixed-point solve are presented as independent, but the validation step reduces to the input construction. No perturbation, omitted-variable, or noisy-estimate analysis is described, producing partial circularity confined to the numerical evidence.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Abstract-only review; full equations and assumptions unavailable. The decomposition of markouts and quadratic approximation appear as modeling choices.

free parameters (1)
  • quadratic value-function approximation
    Used to obtain closed-form quote decomposition; parameters of the quadratic form are not specified in abstract.
axioms (1)
  • domain assumption Adverse post-trade markouts can be decomposed into observable factors plus residual toxicity
    Stated as the key modelling distinction enabling the adjusted hit ratio.

pith-pipeline@v0.9.1-grok · 5817 in / 1357 out tokens · 21459 ms · 2026-06-28T23:19:26.921690+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

4 extracted references · 1 canonical work pages · 1 internal anchor

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    work page internal anchor Pith review Pith/arXiv arXiv 2026