From Arbitrage Removal to Density Extraction: A Model-Free Framework for Short-Dated Options

Aaron Wizman; Gabriel Turinici; Gregory Merran

arxiv: 2605.22792 · v3 · pith:X7QYL37Jnew · submitted 2026-05-21 · 💱 q-fin.CP · q-fin.MF· q-fin.PR

From Arbitrage Removal to Density Extraction: A Model-Free Framework for Short-Dated Options

Aaron Wizman , Gabriel Turinici , Gregory Merran This is my paper

Pith reviewed 2026-06-30 16:08 UTC · model grok-4.3

classification 💱 q-fin.CP q-fin.MFq-fin.PR

keywords risk-neutral densityshort-dated optionsarbitrage removalbid-ask spreadsmodel-free extractionoption chainsimplied volatilitySPX options

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The pith

A model-free pipeline first removes static arbitrage from bid-ask quotes then recovers risk-neutral densities via smoothness and entropy even near expiry.

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

The paper develops a two-step procedure that treats quoted bid and ask prices as hard constraints rather than using midpoints, which often produce infeasible or unstable results when spreads widen near expiry. ARIES iteratively eliminates executable static arbitrage under depth limits, while SEDEx solves an optimization that enforces both smoothness and maximum entropy subject only to the cleaned bounds. Tests on Heston-generated panels and real short-dated SPX chains show the pipeline yields stable densities from a few hours to one week before expiry, including around scheduled announcements. From the densities the authors construct short-tenor implied-volatility smiles without assuming any pricing dynamics.

Core claim

The ARIES+SEDEx pipeline recovers robust risk-neutral densities from short-dated option chains under bid-ask constraints, even near expiry and around macroeconomic announcements, by first removing executable static arbitrage at quoted prices and then optimizing a smooth maximum-entropy density that respects the remaining bounds.

What carries the argument

ARIES (Arbitrage Removal Iterative Executable Strategy) that filters static arbitrage at bid and ask prices under market-depth constraints, followed by SEDEx (Smooth Entropic Density EXtraction) that recovers the density through a smoothness-plus-entropy criterion subject to those cleaned constraints.

If this is right

Densities remain computable and stable even when option premia are small relative to spreads.
The recovered densities support construction of short-dated implied-volatility smiles directly from market quotes.
The procedure runs quickly on both synthetic Heston panels and empirical SPX chains sampled hours to days before expiry.
Densities stay robust across scheduled macroeconomic announcements when bid-ask constraints are respected.

Where Pith is reading between the lines

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

The approach could be applied to intraday updating of densities as fresh quotes arrive, allowing real-time monitoring of tail probabilities.
Traders might use the cleaned densities to identify static arbitrage opportunities that survive the ARIES step.
The same pipeline could be tested on other underlyings with liquid short-dated options to see whether announcement effects appear consistently in the extracted measures.

Load-bearing premise

The smoothness-plus-entropy criterion produces a density close to the true risk-neutral measure rather than an artifact of the regularization choice.

What would settle it

Compare the extracted densities on Heston-simulated data against the known true densities and check whether out-of-sample option prices generated from the densities fall inside the observed bid-ask spreads more consistently than densities obtained from mid quotes or other regularizers.

Figures

Figures reproduced from arXiv: 2605.22792 by Aaron Wizman, Gabriel Turinici, Gregory Merran.

**Figure 1.** Figure 1: Frictionless baseline for 1DTE options. (a) Heston reference risk-neutral density (blue solid line) and SEDEx density (red dots): the two densities are visually indistinguishable at the scale of the figure. (b) Heston call prices (blue line with circles) and call prices implied by SEDEx (orange diamonds): the two series overlap perfectly over the full strike range, up to a numerical tolerance of 10−4 in ab… view at source ↗

**Figure 2.** Figure 2: Arbitrage-free bid–ask setting for 1DTE options. [PITH_FULL_IMAGE:figures/full_fig_p031_2.png] view at source ↗

**Figure 2.** Figure 2: Arbitrage-free bid–ask setting for 1DTE options. [PITH_FULL_IMAGE:figures/full_fig_p032_2.png] view at source ↗

**Figure 3.** Figure 3: Arbitrage-contaminated bid–ask setting for 1DTE options. [PITH_FULL_IMAGE:figures/full_fig_p033_3.png] view at source ↗

**Figure 4.** Figure 4: 1DTE slice on 2023-07-19. (a) Risk-neutral density extracted by SEDEx (red dots). (b) Implied volatility smile obtained by repricing options on a finer strike grid: market ask (red triangles-up), market bid (blue triangles-down), and SEDEx implied volatilities (orange circles). (c) Market bid–ask implied volatilities and SEDEx implied volatilities (orange circles) compared with the SVI benchmark fit (black… view at source ↗

**Figure 5.** Figure 5: Event-driven 1DTE slice on 2022-12-13. (a) Risk-neutral density extracted by SEDEx (red dots), which is slightly bimodal. (b) Implied volatility smile obtained by repricing options on a finer strike grid: market ask (red triangles-up), market bid (blue triangles-down), and SEDEx implied volatilities (orange circles). (c) Market bid–ask implied volatilities and SEDEx implied volatilities (orange circles) co… view at source ↗

**Figure 6.** Figure 6: 0DTE intraday slices on 2023-05-08. (a)–(b) Risk-neutral densities extracted by SEDEx at 10:30 and 15:00 (red dots). (c)–(d) Corresponding implied volatility smiles: market ask (red triangles-up), market bid (blue triangles-down), and SEDEx implied volatilities (orange circles). The bid–ask constraints are satisfied up to a numerical tolerance of 10−6 vol points. 37 [PITH_FULL_IMAGE:figures/full_fig_p03… view at source ↗

**Figure 7.** Figure 7: Representative 7DTE market slice on 2023-04-14. [PITH_FULL_IMAGE:figures/full_fig_p073_7.png] view at source ↗

**Figure 7.** Figure 7: Representative 7DTE market slice on 2023-04-14. [PITH_FULL_IMAGE:figures/full_fig_p074_7.png] view at source ↗

read the original abstract

We study risk-neutral density extraction from short-dated option chains. As expiry approaches, option premia decline and bid--ask spreads can be large relative to prices, making mid quotes particularly uninformative. Stale or asynchronous quotes may also generate potential static arbitrages, rendering standard procedures infeasible or unstable. We develop a model-free pipeline that treats bid-ask quotes as the primitive market constraint. The pipeline consists of two steps. First, a procedure called ``Arbitrage Removal Iterative Executable Strategy'' (ARIES) filters executable static arbitrage at quoted bid and ask prices under market-depth constraints. Second, the ``Smooth Entropic Density EXtraction'' (SEDEx) then recovers the density through a criterion leveraging smoothness and entropy under bid-ask constraints. We test the pipeline on synthetic Heston panels and short-dated SPX option data, sampled from a few hours to one week before expiry. Computation is fast and returns robust densities across various market conditions, including scheduled macroeconomic announcements. As an empirical application, we use the recovered densities to construct short dated implied-volatility smiles.

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.

Desk Editor's Note private letter to a colleague

The paper gives a two-step pipeline that cleans executable arbitrage from short-dated bid-ask quotes then extracts a density via entropy plus smoothness, but the abstract supplies no numbers to check whether the regularization recovers the actual risk-neutral measure.

read the letter

The core contribution is a practical pipeline for short-dated options where wide spreads and stale quotes often make mid prices unusable. ARIES first removes static arbitrage that can actually be executed given quoted depths. SEDEx then solves for a density that stays inside the cleaned bid-ask bounds while maximizing entropy and penalizing roughness.

This combination is applied to both Heston synthetic panels and real SPX chains from a few hours to a week before expiry, including around macro announcements. The method runs quickly and produces densities that can be turned into implied-volatility smiles. That focus on the near-expiry regime, where standard extractors tend to fail, is the part that feels new.

The soft spot is the lack of quantitative checks. The abstract states that the pipeline returns robust densities, yet it gives no error metrics, no comparison against other extractors, and no demonstration that the smoothness-plus-entropy choice stays close to the true measure rather than just producing a plausible smooth object. No-arbitrage constraints alone do not pin down a unique density, so the regularization matters.

The work is aimed at quant practitioners who need usable short-term densities from noisy market data. A reader who already works with option-implied distributions would find a concrete method worth trying on their own chains.

It deserves peer review. The problem is real, the steps are described clearly enough to reproduce, and the empirical tests on both synthetic and live data give a starting point for referees to evaluate.

Referee Report

3 major / 2 minor

Summary. The manuscript develops a model-free two-step pipeline (ARIES followed by SEDEx) for extracting risk-neutral densities from short-dated option chains. ARIES iteratively removes executable static arbitrages from bid-ask quotes subject to market-depth constraints; SEDEx then recovers a density by maximizing entropy subject to a smoothness penalty and the cleaned bid-ask constraints. The pipeline is tested on synthetic Heston panels and empirical short-dated SPX data (hours to one week to expiry, including around announcements) and applied to construct implied-volatility smiles.

Significance. If validated, the approach would address a practical gap in density extraction where wide spreads and stale quotes render standard methods unstable near expiry. Treating executable bid-ask quotes as primitives and emphasizing computational speed are strengths. The absence of quantitative error metrics, baseline comparisons, or falsification tests against the true measure in the synthetic experiments limits the ability to assess whether the regularization produces the risk-neutral density or an artifact.

major comments (3)

[§4] §4 (SEDEx formulation): the central claim that the smoothness-plus-entropy objective recovers a density close to the true risk-neutral measure (rather than an artifact of the chosen regularization) is not supported by any theoretical convergence result or numerical experiment that varies the penalty weight and checks consistency with the Heston ground truth; this assumption is load-bearing for the pipeline's validity.
[§5.2] §5.2 (synthetic Heston tests): no quantitative performance metrics (e.g., integrated squared error, Kullback-Leibler divergence, or coverage of the true density) or comparisons to alternative density-extraction methods are reported, so the statement that the pipeline 'returns robust densities' cannot be evaluated.
[§6] §6 (empirical SPX application): the recovered densities are used to build implied-volatility smiles, but no diagnostic is shown that the SEDEx output satisfies the original bid-ask constraints after optimization or that the smoothness penalty does not systematically bias the left or right tail near expiry.

minor comments (2)

Notation for the bid-ask depth constraints in ARIES should be defined once and used consistently across sections.
Figure captions for the synthetic and empirical density plots should include the exact values of the smoothness and entropy weights used.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive feedback, which highlights important areas for strengthening the validation of our ARIES+SEDEx pipeline. We address each major comment below and commit to revisions that add the requested quantitative checks and diagnostics while preserving the model-free, practical focus of the work.

read point-by-point responses

Referee: [§4] §4 (SEDEx formulation): the central claim that the smoothness-plus-entropy objective recovers a density close to the true risk-neutral measure (rather than an artifact of the chosen regularization) is not supported by any theoretical convergence result or numerical experiment that varies the penalty weight and checks consistency with the Heston ground truth; this assumption is load-bearing for the pipeline's validity.

Authors: We agree that no theoretical convergence result is provided, as the method prioritizes computational tractability and market-data fidelity over asymptotic guarantees. To address the concern empirically, the revised manuscript will include new experiments that vary the smoothness penalty coefficient over a wide range and report quantitative distances (L2 norm and KL divergence) to the known Heston risk-neutral density. These will demonstrate consistency of the recovered densities with the ground truth for the chosen regularization. revision: yes
Referee: [§5.2] §5.2 (synthetic Heston tests): no quantitative performance metrics (e.g., integrated squared error, Kullback-Leibler divergence, or coverage of the true density) or comparisons to alternative density-extraction methods are reported, so the statement that the pipeline 'returns robust densities' cannot be evaluated.

Authors: We accept this point. The revision will add integrated squared error, Kullback-Leibler divergence, and coverage metrics for the synthetic Heston panels. We will also include comparisons against standard alternatives (e.g., cubic-spline interpolation of call prices followed by second differentiation, and pure maximum-entropy without smoothness) to allow direct evaluation of the pipeline's performance. revision: yes
Referee: [§6] §6 (empirical SPX application): the recovered densities are used to build implied-volatility smiles, but no diagnostic is shown that the SEDEx output satisfies the original bid-ask constraints after optimization or that the smoothness penalty does not systematically bias the left or right tail near expiry.

Authors: We will incorporate the requested checks. The revised empirical section will report the maximum and average constraint violations after SEDEx optimization (measured in price units relative to bid-ask spreads) and will include sensitivity plots that vary the smoothness weight while tracking changes in the left and right tails of the density and the resulting implied-volatility smile wings. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation treats quotes as primitives and applies explicit regularization

full rationale

The pipeline defines ARIES as arbitrage removal from bid-ask quotes and SEDEx as an explicit optimization (smoothness + entropy subject to those quotes). No equation reduces the output density to a fitted parameter defined inside the paper, no self-citation is invoked as a uniqueness theorem, and the criterion is presented as a modeling choice rather than derived from the inputs by construction. The approach is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Abstract-only review; the pipeline implicitly assumes that (1) static arbitrage can be exhaustively detected and removed at quoted bid/ask levels under depth constraints and (2) a smoothness-plus-entropy objective yields a density consistent with the true risk-neutral measure. No free parameters or invented entities are named.

axioms (2)

domain assumption Bid and ask quotes plus market depth constitute the complete primitive market constraint for static arbitrage removal.
Stated in the description of ARIES as treating 'bid-ask quotes as the primitive market constraint'.
domain assumption A density maximizing entropy subject to smoothness and the cleaned bid-ask constraints is the appropriate recovered risk-neutral density.
Core of the SEDEx step; no justification or alternative criteria are discussed in the abstract.

pith-pipeline@v0.9.1-grok · 5732 in / 1423 out tokens · 32503 ms · 2026-06-30T16:08:48.521982+00:00 · methodology

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Reference graph

Works this paper leans on

2 extracted references

[1]

−1 2 + X−m ˜σ2 2# .(222) 78 Using the moments of a Gaussian distribution and simplifying the resulting expres- sion, one obtains E

in (52), we have q′ 0 +q ′ 1 =m, q ′ 0K ′ +q ′ 1K1 =m ¯K.(163) Moreover, multiplying (51) bym= 1−Q 1 yields the identity m ¯K= (1−Q 0)K0 + (Q0 −Q 1)K1.(164) Combining (162)–(164) with (49) gives Eν[ST ] = (1−Q 0)K0 + NX j=1 Kj(Qj−1 −Q j) +K N+1 QN .(165) A straightforward telescoping computation rewrites the right-hand side as (1−Q 0)K0 + NX j=1 Kj(Qj−1 −...

1936
[2]

andq ∗ =− 1 T ln ˆβ∗ 0 S0 ! .(242) Finally, we address the specific case of ultra-short-dated options. As the time to expiration approaches zero, the mapping (242) becomes ill-conditioned: a tiny estimation error inβ 1 can translate into a large annualizedrdue to the factor 1/T (and similarly forβ 0 andq). In this regime, discounting effects are negligibl...

[1] [1]

−1 2 + X−m ˜σ2 2# .(222) 78 Using the moments of a Gaussian distribution and simplifying the resulting expres- sion, one obtains E

in (52), we have q′ 0 +q ′ 1 =m, q ′ 0K ′ +q ′ 1K1 =m ¯K.(163) Moreover, multiplying (51) bym= 1−Q 1 yields the identity m ¯K= (1−Q 0)K0 + (Q0 −Q 1)K1.(164) Combining (162)–(164) with (49) gives Eν[ST ] = (1−Q 0)K0 + NX j=1 Kj(Qj−1 −Q j) +K N+1 QN .(165) A straightforward telescoping computation rewrites the right-hand side as (1−Q 0)K0 + NX j=1 Kj(Qj−1 −...

1936

[2] [2]

andq ∗ =− 1 T ln ˆβ∗ 0 S0 ! .(242) Finally, we address the specific case of ultra-short-dated options. As the time to expiration approaches zero, the mapping (242) becomes ill-conditioned: a tiny estimation error inβ 1 can translate into a large annualizedrdue to the factor 1/T (and similarly forβ 0 andq). In this regime, discounting effects are negligibl...