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arxiv: 2605.22792 · v1 · 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 2026-05-22 02:34 UTC · model grok-4.3

classification 💱 q-fin.CP q-fin.MFq-fin.PR
keywords risk-neutral densityshort-dated optionsstatic arbitrage removalentropy maximizationbid-ask spreadsimplied volatility smilemodel-free methodsSPX options
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The pith

The ARIES-SEDEx pipeline recovers robust risk-neutral densities from short-dated option data even with large bid-ask spreads and static arbitrages.

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

This paper introduces a model-free two-step pipeline to extract risk-neutral densities from short-dated options where wide spreads and stale quotes make standard methods unstable. The first step, ARIES, iteratively removes executable static arbitrages while respecting quoted bid and ask prices plus market depth. The second step, SEDEx, recovers the density by maximizing entropy while enforcing smoothness and staying inside the cleaned bid-ask bounds. Tests on Heston simulations and real SPX chains from hours to one week before expiry show stable results even around announcements, and the densities support construction of short-dated implied-volatility smiles.

Core claim

Treating bid-ask quotes as the primitive constraint, first filtering static arbitrage via an iterative executable strategy at those prices, and then optimizing a smoothness-plus-entropy objective under the resulting bounds produces reliable risk-neutral densities from short-dated option data without any parametric assumption on the underlying process.

What carries the argument

The ARIES-SEDEx pipeline, in which ARIES removes executable static arbitrages at bid and ask prices under depth constraints and SEDEx extracts the density through a smoothness and entropy criterion respecting those constraints.

If this is right

  • Robust densities can be recovered even when raw mid quotes are uninformative due to large spreads.
  • The method remains stable across market conditions including scheduled macroeconomic announcements.
  • Computation is fast enough for practical use on short-dated chains.
  • The extracted densities directly enable construction of short-dated implied-volatility smiles.

Where Pith is reading between the lines

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

  • The cleaned densities may improve short-term hedging or exotic pricing by supplying better local volatility or tail estimates.
  • Applying the same pipeline to other underlyings could test whether liquidity effects near expiry are systematic.
  • Comparing short-dated densities to those from longer expiries on the same day could quantify term-structure features in the risk-neutral measure.

Load-bearing premise

That the combination of smoothness and entropy maximization under the post-ARIES bid-ask constraints produces a unique or stable density without material bias relative to the true risk-neutral measure.

What would settle it

Generate synthetic option quotes from a known model such as Heston, insert realistic bid-ask spreads and artificial static arbitrages, run the full pipeline, and verify whether the recovered density matches the model's known risk-neutral density within small error.

Figures

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

Figure 1
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. Figure 2: Arbitrage-free bid–ask setting for 1DTE options. [PITH_FULL_IMAGE:figures/full_fig_p031_2.png] view at source ↗
Figure 3
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. 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. 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. Figure 6: 0DTE intraday slices on 2023-05-08. (a)–(b) Risk-neutral densities ex￾tracted 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 satis￾fied 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. Figure 7: Representative 7DTE market slice on 2023-04-14. [PITH_FULL_IMAGE:figures/full_fig_p073_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.

Referee Report

3 major / 2 minor

Summary. The paper proposes a two-step model-free pipeline for extracting risk-neutral densities from short-dated option chains with large bid-ask spreads and potential static arbitrages. ARIES iteratively removes executable static arbitrages while respecting quoted bid-ask prices and market-depth constraints; SEDEx then recovers a density by maximizing entropy subject to a smoothness penalty and the post-ARIES bid-ask inequality constraints on call prices. The method is tested on synthetic Heston panels and real short-dated SPX data (hours to one week to expiry), with an application to constructing implied-volatility smiles.

Significance. If the central claim holds, the framework offers a practical, model-free route to stable risk-neutral densities when conventional mid-price methods fail due to wide spreads or stale quotes. The explicit use of bid-ask intervals as primitives and the fast computation are strengths for near-expiry applications in pricing and risk management. The absence of quantitative error metrics in the reported tests, however, limits the ability to gauge how much bias or variance the pipeline introduces relative to the true measure.

major comments (3)
  1. [Abstract / synthetic tests section] Abstract and synthetic-experiment description: the claim that the pipeline 'returns robust densities' is not supported by any reported quantitative metrics (e.g., integrated squared error, Kullback-Leibler divergence, or moment bias) between the recovered density and the known Heston density across varying spread widths. Without these, it is impossible to assess whether the max-entropy solution under loose post-ARIES constraints materially understates skewness or kurtosis.
  2. [SEDEx description] SEDEx formulation: when bid-ask intervals are wide (typical for short-dated options), the entropy-maximization objective plus smoothness penalty can still favor a near-Gaussian density; the manuscript does not provide a proof or numerical demonstration that the recovered density remains close to the true risk-neutral measure rather than defaulting to the least-informative distribution consistent with the wide bounds.
  3. [Empirical application] Empirical section: no baseline comparisons (e.g., to spline-based or parametric density extraction methods) are shown on the same SPX chains, making it difficult to judge whether the ARIES+SEDEx pipeline improves upon simpler arbitrage-removal-plus-interpolation approaches.
minor comments (2)
  1. [ARIES procedure] Clarify the precise definition of 'market-depth constraints' used inside ARIES and how they translate into the inequality system passed to SEDEx.
  2. [Numerical results] The abstract states that computation is 'fast'; a table or paragraph reporting run times on the SPX panels would strengthen this claim.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed comments. We address each major comment point by point below, indicating the revisions we will make to strengthen the manuscript.

read point-by-point responses

  1. Referee: [Abstract / synthetic tests section] Abstract and synthetic-experiment description: the claim that the pipeline 'returns robust densities' is not supported by any reported quantitative metrics (e.g., integrated squared error, Kullback-Leibler divergence, or moment bias) between the recovered density and the known Heston density across varying spread widths. Without these, it is impossible to assess whether the max-entropy solution under loose post-ARIES constraints materially understates skewness or kurtosis.

    Authors: We agree that quantitative error metrics are necessary to substantiate the robustness claim in the synthetic experiments. In the revised manuscript we will add explicit performance tables reporting integrated squared error, Kullback-Leibler divergence, and biases in skewness and kurtosis between the recovered densities and the true Heston density, evaluated across a grid of bid-ask spread widths. These metrics will directly address whether higher moments are materially understated under the post-ARIES constraints. revision: yes

  2. Referee: [SEDEx description] SEDEx formulation: when bid-ask intervals are wide (typical for short-dated options), the entropy-maximization objective plus smoothness penalty can still favor a near-Gaussian density; the manuscript does not provide a proof or numerical demonstration that the recovered density remains close to the true risk-neutral measure rather than defaulting to the least-informative distribution consistent with the wide bounds.

    Authors: We acknowledge that maximum-entropy optimization produces the least-informative distribution consistent with the supplied constraints. The ARIES step, however, supplies tightened bid-ask intervals that already incorporate executable arbitrage removal and market-depth limits; the smoothness penalty further regularizes the solution away from pure Gaussian behavior. A general proof of proximity to the unknown true measure is not feasible without additional assumptions on the data-generating process. We will therefore add numerical demonstrations in the revised SEDEx section that compare recovered densities to the known Heston measure under successively wider spreads, showing preservation of skewness and kurtosis beyond what an unconstrained Gaussian would exhibit. revision: partial

  3. Referee: [Empirical application] Empirical section: no baseline comparisons (e.g., to spline-based or parametric density extraction methods) are shown on the same SPX chains, making it difficult to judge whether the ARIES+SEDEx pipeline improves upon simpler arbitrage-removal-plus-interpolation approaches.

    Authors: We concur that side-by-side comparisons on identical SPX chains would clarify the incremental benefit of the full pipeline. In the revised empirical section we will include results for the same short-dated SPX option chains using (i) cubic-spline interpolation on mid prices after standard arbitrage removal and (ii) a parametric mixture-of-lognormals density fit. Comparative metrics will include smoothness of the extracted implied-volatility smiles, stability across consecutive trading hours, and computational cost, thereby quantifying the advantages of ARIES+SEDEx relative to these simpler baselines. revision: yes

Circularity Check

0 steps flagged

No significant circularity: model-free pipeline anchored to observable constraints

full rationale

The ARIES-SEDEx pipeline is defined directly from quoted bid-ask prices and market-depth constraints as primitives. ARIES removes executable static arbitrages at those prices; SEDEx then solves a smoothness-plus-entropy optimization subject to the resulting inequality constraints on call prices. No equation reduces the extracted density to a fitted parameter, a self-referential definition, or a load-bearing self-citation. The method is explicitly model-free, with no imported uniqueness theorems or ansatzes from prior author work indicated. Tests on synthetic Heston data and SPX quotes provide external benchmarks rather than internal consistency checks that would force the result by construction. This is the normal, self-contained case for a constraint-based extraction procedure.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The framework rests on standard risk-neutral valuation and the interpretation of quoted bid-ask as hard executable constraints; no new free parameters, invented entities, or ad-hoc axioms are introduced in the abstract description.

axioms (2)
  • domain assumption Risk-neutral pricing holds and option prices are expectations under the risk-neutral measure.
    Foundational premise for any density extraction from option quotes.
  • domain assumption Bid and ask quotes with associated depths constitute the primitive market constraints that must be respected.
    Explicitly stated as the starting point for the ARIES filtering step.

pith-pipeline@v0.9.0 · 5732 in / 1285 out tokens · 44720 ms · 2026-05-22T02:34:43.832040+00:00 · methodology

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