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arxiv: 2606.12872 · v2 · pith:3PTDXMD5new · submitted 2026-06-11 · 💱 q-fin.PR

Non-Spanning Identification of Scheduled Event Risk in Option Pricing

Tenghan Zhong This is my paper

Pith reviewed 2026-06-27 05:20 UTC · model grok-4.3

classification 💱 q-fin.PR
keywords SPX optionsscheduled event riskoption pricingvolatility surfacejump modelsFOMCCPINFP
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The pith

Non-spanning expiries separate the no-event volatility surface from scheduled event jumps in option pricing.

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

The paper establishes that expiries avoiding scheduled macro announcements can identify a clean continuous volatility surface, while event-spanning quotes separately calibrate deterministic-time jumps for FOMC, CPI, and NFP decisions. This separation prevents the surface from absorbing event premia, which would otherwise leave the jump component unidentified. On PM-settled SPX options from 2022 to 2025, adding Gaussian or two-component mixture jumps under this protocol reduces held-out pricing errors, with clearest gains in median errors and for volatility combinations such as straddles and strangles. The approach also shows stronger identification for CPI and FOMC than for NFP, and a stress test confirms that mixing event quotes into the surface produces misleading performance by absorbing rather than isolating risk.

Core claim

By restricting the no-event volatility surface fit to non-spanning expiries and using event-spanning training quotes only for jump calibration, Gaussian and two-component mixture jumps deliver improved held-out pricing performance on event-spanning SPX options, most notably in robust median errors and non-directional strategies, while a contaminated-surface test demonstrates that absorbing event premia into the surface produces strong but spurious results.

What carries the argument

The non-spanning identification protocol, which fits the continuous volatility surface exclusively on non-event-spanning expiries and calibrates scheduled jumps on event-spanning quotes.

If this is right

  • Gaussian and two-component mixture jumps calibrated under the protocol reduce held-out pricing errors on event-spanning quotes.
  • The largest improvements appear in robust median errors and in volatility-sensitive combinations such as straddles and strangles rather than directional risk reversals.
  • Fitting the no-event surface with event-spanning quotes included produces apparently strong performance by absorbing premia instead of isolating jumps.
  • Scheduled-jump identification performs best for CPI and FOMC events and more weakly for NFP.
  • Amortized mixture models show limited cross-event transfer, with pure leave-one-event-out versions improving some volatility errors but not all pricing metrics.

Where Pith is reading between the lines

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

  • The same non-spanning separation could be tested on single-stock options around earnings dates to isolate firm-specific event risk from the background surface.
  • Models that skip this separation may systematically over-attribute price variation around announcements to continuous volatility rather than discrete jumps.
  • Extending the protocol to additional announcement types or to intraday option data could further isolate the size and timing of the jump component.

Load-bearing premise

Expiries that avoid scheduled events can produce a volatility surface entirely free of event premia.

What would settle it

A model that fits the no-event surface to a mix of spanning and non-spanning quotes and then matches or exceeds the separated protocol's held-out performance on event quotes without any explicit jump component would falsify the identification claim.

Figures

Figures reproduced from arXiv: 2606.12872 by Tenghan Zhong.

Figure 1
Figure 1. Figure 1: Non-spanning identification for scheduled event risk. Contracts with [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Event-level paired bootstrap differences in SPX specification with continuous IV cap [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Option-combination pricing errors in the main SPX [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Scale-shape attribution for scheduled event-jump [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
read the original abstract

Short-dated index options make scheduled macro-announcement risk visible in market prices, but visibility does not imply identification: a flexible no-event surface fitted to event-spanning quotes can absorb event premia, while a jump calibrated without event-spanning quotes is unidentified. To separate the continuous surface from the scheduled jump, we model Federal Open Market Committee (FOMC) decisions, Consumer Price Index (CPI) releases, and nonfarm payroll (NFP) reports as deterministic-time jumps in risk-neutral option pricing and propose a non-spanning identification protocol. Non-spanning expiries identify the no-event volatility surface, event-spanning training quotes calibrate the scheduled jump, and held-out event-spanning quotes are used only for pricing evaluation. On PM-settled S\&P 500 index (SPX) options from May 2022 to August 2025, Gaussian and two-component mixture jumps improve held-out event-spanning pricing, with the clearest gains in robust median pricing errors and in event-volatility option combinations (straddles and strangles) rather than directional risk reversals. A contaminated-surface stress test confirms the identification concern: allowing event-spanning training quotes into the no-event surface fit produces strong held-out performance by absorbing event premia rather than identifying scheduled jump risk. An amortized mixture density network (MDN) benchmark shows limited cross-event transfer: pure leave-one-event-out amortization reduces implied-volatility errors but not mean dollar or mean spread-normalized pricing errors, while the scale-calibrated variant restores Gaussian-level performance yet remains below event-specific mixture calibration. Scheduled-jump identification is strongest for CPI and FOMC and weaker for NFP.

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 / 2 minor

Summary. The paper claims that scheduled event risk in short-dated index options can be identified separately from the continuous volatility surface using a non-spanning protocol: non-spanning expiries fit the no-event surface, event-spanning training quotes calibrate Gaussian or mixture jump parameters for FOMC, CPI, and NFP events, and held-out event-spanning quotes evaluate pricing performance. Empirical results on PM-settled SPX options from May 2022 to August 2025 show improvements in held-out pricing, particularly robust median errors and event-volatility combinations like straddles and strangles. The contaminated-surface stress test confirms that violating the protocol by allowing event-spanning quotes into the surface fit leads to absorption of event premia rather than genuine identification. Comparisons to amortized MDN benchmarks are also presented.

Significance. If the central claim holds, the work provides a practical and validated method for separating scheduled jump risk from diffusive volatility in option pricing, which is significant for accurate pricing and hedging around macro announcements. The inclusion of a stress test that directly tests the identification vulnerability is a strength, as is the use of held-out data for evaluation and the comparison to machine learning benchmarks. This could influence how event risk is modeled in quantitative finance.

major comments (2)
  1. [Identification protocol (as described in abstract and methods)] The central assumption that non-spanning expiries identify a clean no-event volatility surface uncontaminated by scheduled event premia is load-bearing for the identification claim; while the contaminated-surface stress test shows the consequence of violation, the manuscript should specify the exact criteria and distance thresholds used to select non-spanning expiries to allow replication and assess robustness.
  2. [Empirical results on jump calibration] Jump parameters are fitted directly to the event-spanning training quotes, which raises the question of how much of the held-out improvement is due to the non-spanning separation versus the flexibility of the jump model itself; a comparison to fitting jumps without the non-spanning surface would clarify if the protocol adds value beyond the jump specification.
minor comments (2)
  1. [Abstract] The abstract mentions 'the clearest gains in robust median pricing errors'; it would be helpful to define 'robust median' explicitly or reference the table where it is reported.
  2. [MDN benchmark] The description of the amortized mixture density network benchmark could include more details on the network architecture and training to facilitate comparison.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive evaluation and the recommendation for minor revision. The comments are constructive and we address each one below, indicating the revisions that will be incorporated.

read point-by-point responses

  1. Referee: [Identification protocol (as described in abstract and methods)] The central assumption that non-spanning expiries identify a clean no-event volatility surface uncontaminated by scheduled event premia is load-bearing for the identification claim; while the contaminated-surface stress test shows the consequence of violation, the manuscript should specify the exact criteria and distance thresholds used to select non-spanning expiries to allow replication and assess robustness.

    Authors: We agree that explicit specification of the selection criteria is required for replication. In the revised manuscript we will add a dedicated paragraph in Section 3 detailing the precise distance thresholds (minimum calendar days from any scheduled event) and any auxiliary filters applied to designate non-spanning expiries. We will also include a short robustness table showing how pricing metrics change when these thresholds are varied by ±2 days. revision: yes

  2. Referee: [Empirical results on jump calibration] Jump parameters are fitted directly to the event-spanning training quotes, which raises the question of how much of the held-out improvement is due to the non-spanning separation versus the flexibility of the jump model itself; a comparison to fitting jumps without the non-spanning surface would clarify if the protocol adds value beyond the jump specification.

    Authors: The contaminated-surface stress test already isolates the role of the protocol by showing that, when event-spanning quotes are allowed into the surface fit, the model absorbs event premia into the diffusive surface rather than identifying the jump, producing strong in-sample but non-identifying results. To make the incremental contribution of the non-spanning step fully transparent, the revision will add a direct side-by-side benchmark: jump parameters calibrated to event-spanning quotes on top of a contaminated surface versus the same jump model on top of the non-spanning surface, with held-out metrics reported for both. revision: yes

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper's central protocol separates no-event surface calibration (non-spanning expiries) from jump calibration (event-spanning training quotes) with explicit held-out evaluation and a contaminated-surface stress test that isolates absorption effects. No step reduces a claimed prediction or identification result to its own fitted inputs by construction; the held-out gains and stress-test contrast are independent checks rather than tautological. No self-citation load-bearing steps or ansatz smuggling appear in the described chain.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

Based on abstract only; the model relies on standard risk-neutral pricing and the assumption that scheduled events can be treated as deterministic-time jumps whose size is identified separately from the continuous surface.

free parameters (1)
  • Gaussian and mixture jump parameters
    Calibrated to event-spanning training quotes for each announcement type
axioms (2)
  • standard math Risk-neutral pricing holds for the option surface
    Invoked as the modeling framework for both continuous surface and jumps
  • domain assumption Scheduled events occur at deterministic times and can be isolated from the continuous process
    Central modeling choice stated in the abstract

pith-pipeline@v0.9.1-grok · 5824 in / 1454 out tokens · 24156 ms · 2026-06-27T05:20:28.154333+00:00 · methodology

discussion (0)

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Reference graph

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