Tuning in to Frequencies: How Global Assets Align with U.S. Put-Call Parity Residuals

Useong Shin

arxiv: 2604.19605 · v7 · pith:IBIQQRXAnew · submitted 2026-04-21 · 💱 q-fin.GN

Tuning in to Frequencies: How Global Assets Align with U.S. Put-Call Parity Residuals

Useong Shin This is my paper

Pith reviewed 2026-05-21 00:45 UTC · model grok-4.3

classification 💱 q-fin.GN

keywords put-call parityresidualsglobal assetsP-Q alignmentcapital constraintsSPXRUToutside options

0 comments

The pith

Global assets explain US put-call parity residuals after funding and volatility controls.

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

The paper tests whether the carry gap in US index put-call parity is fully accounted for by OIS funding, volatility, trading frictions, and financial conditions, or whether it also reflects residual outside-option information from global markets. Adding the ETFs IEFA, IGOV, and IAU as regressors improves both in-sample and leave-one-year-out fit once US-centered controls are in place. These gains remain after broad-dollar neutralization, alternative blocks, PCA, residualization, and nested horizon selection. The results indicate that finite-capital enforcement of parity incorporates physical-measure investment opportunities rather than operating solely as a risk-neutral no-arbitrage relation at terminal payoff.

Core claim

Put-call parity is risk-neutral only at terminal payoff, yet its enforcement uses capital and is therefore path-dependent. After controlling for OIS-based funding, volatility, trading frictions, and financial-condition variables, the residuals in the SPX-RUT carry gap still align with outside-option information contained in the global assets IEFA, IGOV, and IAU. The alignment survives multiple robustness layers and supports a reduced-form P-Q link in which parity enforcement reflects physical-measure investment opportunities.

What carries the argument

The incremental explanatory power of global asset returns (IEFA, IGOV, IAU) added after US-centered controls and robustness transformations to account for the put-call parity residual.

If this is right

US index parity residuals carry information about international investment opportunities once local controls are removed.
Arbitrageurs with finite capital weigh global alternatives when deciding whether to enforce put-call parity.
Models that treat parity as a pure risk-neutral condition at payoff miss the physical-measure channels that actually bind enforcement.
The same residual logic should apply to other capital-constrained derivative relationships across borders.

Where Pith is reading between the lines

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

If the alignment holds, flows into global ETFs could help forecast near-term shifts in US index parity residuals.
Similar patterns may appear in equity options or futures on other major indices where capital is allocated globally.

Load-bearing premise

The added global assets supply independent outside-option information that is not already captured by the US-centered controls or by the robustness procedures.

What would settle it

Finding no improvement in explanatory power or out-of-sample fit when the global assets are added to fresh data windows or to specifications that further orthogonalize against US factors would falsify the claim of residual alignment.

Figures

Figures reproduced from arXiv: 2604.19605 by Useong Shin.

**Figure 4.1.** Figure 4.1: Incremental R2 by lookback horizon for ETFs representing the major asset classes. The effective lookback horizon at which each asset aligns with the carry gap differs sharply across assets. The upper panel shows SPX results; the lower panel, RUT. The key feature of [PITH_FULL_IMAGE:figures/full_fig_p011_4_1.png] view at source ↗

**Figure 4.2.** Figure 4.2: OLS slope time series for the three selected ETFs. Each series is the log OLS [PITH_FULL_IMAGE:figures/full_fig_p013_4_2.png] view at source ↗

**Figure 4.3.** Figure 4.3: Incremental R2 by lookback horizon for the three selected ETFs. The upper panel shows SPX results; the lower panel, RUT [PITH_FULL_IMAGE:figures/full_fig_p014_4_3.png] view at source ↗

**Figure 5.1.** Figure 5.1: Maturity-pooled daily fit: baseline separate specification versus 3ETF extended [PITH_FULL_IMAGE:figures/full_fig_p016_5_1.png] view at source ↗

**Figure 5.2.** Figure 5.2: Fitted versus actual scatter plots: baseline versus 3ETF extended specification. [PITH_FULL_IMAGE:figures/full_fig_p017_5_2.png] view at source ↗

**Figure 5.3.** Figure 5.3: Year-by-year LOYO out-of-sample R2 : baseline separate specification versus 3ETF extended specification. Bars in each panel show the holdout-year out-of-sample R2 . The 3ETF specification delivers higher R2 than the baseline in many holdout years in both markets [PITH_FULL_IMAGE:figures/full_fig_p021_5_3.png] view at source ↗

read the original abstract

Put-call parity is risk-neutral at terminal payoff, but its enforcement is path-dependent and capital-using. I test whether the SPX and RUT carry gap is explained by OIS-based funding, volatility, trading-friction, and financial-condition variables, or also by residual outside-option information. Adding IEFA, IGOV, and IAU improves in-sample and leave-one-year-out fit after U.S.-centered controls. Gains survive broad-dollar neutralization, alternative blocks, PCA, residualization, and nested horizon selection. Results support reduced-form P-Q alignment: finite-capital parity enforcement reflects physical-measure investment opportunities, not payoff-level no-arbitrage failure.

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

Global ETFs add some fit to US put-call parity residuals beyond standard controls, but the independence of that signal from overlapping factors is not fully shown.

read the letter

The main thing to know is that adding IEFA, IGOV, and IAU improves the explanation of SPX-RUT carry-gap residuals after OIS funding, volatility, trading-friction, and financial-condition controls, and the improvement holds under dollar neutralization, PCA, residualization, and leave-one-year-out checks. This is presented as evidence that finite-capital parity enforcement tracks physical-measure outside options rather than pure risk-neutral violations. The work is a straightforward empirical extension that applies established regression tools to a fresh combination of US residuals and a small set of global ETFs. The multiple robustness layers and out-of-sample tests are the parts that look solid and show some effort to avoid obvious overfitting. Credit for testing whether these assets supply incremental power instead of stopping at US-only variables. The soft spot is the assumption that the global series bring information orthogonal to the controls. Shared global risk premia or liquidity channels could still drive the extra fit even after the listed procedures, and the abstract does not report incremental R-squared, VIF, or post-robustness factor loadings that would confirm distinct contributions. If the full manuscript has those diagnostics, the interpretation would sit on firmer ground; without them the reduced-form P-Q alignment claim rests on an unverified independence step. This paper is for readers working on limits to arbitrage and cross-market capital constraints. Someone already following empirical work on option parity and outside options could extract a modest data point from the robustness results. I would send it to peer review. The question is clear, the methods are replicable, and the checks are sufficient to merit referee time even if revisions are needed on the incremental contribution.

Referee Report

1 major / 2 minor

Summary. The manuscript tests whether residuals from put-call parity on SPX and RUT are explained solely by U.S.-centered controls (OIS funding, volatility, trading frictions, financial conditions) or also by outside-option information from global assets (IEFA, IGOV, IAU). It reports that adding the global series improves both in-sample and leave-one-year-out fit; these gains survive dollar neutralization, alternative blocks, PCA, residualization, and nested horizon selection. The central conclusion is that finite-capital parity enforcement reflects physical-measure investment opportunities rather than a failure of payoff-level no-arbitrage.

Significance. If the result holds after the requested diagnostics, the work supplies concrete empirical support for reduced-form P-Q alignment under capital constraints, showing how global physical-measure opportunities can influence U.S. option-market residuals. The manuscript already includes leave-one-year-out validation and a battery of robustness procedures (dollar neutralization, PCA, residualization), which are positive features for an empirical finance paper.

major comments (1)

[Robustness and results sections] The robustness procedures (dollar neutralization, PCA, residualization) are described as preserving the gains from the global assets, yet no post-robustness diagnostics are reported that directly test orthogonality. Incremental R², VIF, or factor-loading tables after these steps would be required to confirm that IEFA/IGOV/IAU supply explanatory power independent of shared global-factor loadings already captured by the U.S. controls.

minor comments (2)

[Methods] Clarify the exact construction of the 'broad-dollar neutralization' variable and whether it is applied before or after the PCA step.
[Abstract] The abstract refers to 'nested horizon selection'; a short footnote or sentence explaining the nesting criterion would aid readability.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript. The suggestion for additional post-robustness diagnostics is well taken and will be incorporated to strengthen the evidence on the independent contribution of the global assets.

read point-by-point responses

Referee: [Robustness and results sections] The robustness procedures (dollar neutralization, PCA, residualization) are described as preserving the gains from the global assets, yet no post-robustness diagnostics are reported that directly test orthogonality. Incremental R², VIF, or factor-loading tables after these steps would be required to confirm that IEFA/IGOV/IAU supply explanatory power independent of shared global-factor loadings already captured by the U.S. controls.

Authors: We appreciate this point. The manuscript states that the fit improvements from the global series survive dollar neutralization, PCA, residualization, and related checks, but we agree that explicit post-procedure diagnostics would better demonstrate orthogonality to any shared global factors already absorbed by the U.S. controls. In the revised version we will add incremental R² tables and VIF statistics computed after each robustness step. Where feasible we will also report relevant factor loadings to confirm that IEFA, IGOV, and IAU retain explanatory power beyond the U.S.-centered variables. revision: yes

Circularity Check

0 steps flagged

No significant circularity; empirical tests are self-contained

full rationale

The paper conducts an empirical regression analysis testing whether global assets (IEFA, IGOV, IAU) add explanatory power to SPX/RUT put-call parity residuals after U.S.-centered controls, with reported improvements surviving dollar neutralization, PCA, residualization, and out-of-sample checks. No equations or steps reduce a claimed prediction or result to a fitted input by construction, no self-definitional loops appear, and no load-bearing self-citations substitute for independent verification. The central interpretation follows from the reported incremental fits and robustness procedures rather than from re-labeling or re-deriving the inputs themselves.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based solely on the abstract, no explicit free parameters, axioms, or invented entities are stated. The central claim rests on the unstated assumption that the chosen global assets and robustness procedures isolate outside-option information without residual confounding.

pith-pipeline@v0.9.0 · 5634 in / 1119 out tokens · 45300 ms · 2026-05-21T00:45:39.618607+00:00 · methodology

Review history (3 revisions) →

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

The carry gap is a Q-measure object... whether this Q-measure carry-space residual is separable from P-measure outside-option proxies... reduced-form P–Q alignment
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

GBM term = path-risk scale × opportunity-cost component... replaced the OIS rate... with low-frequency outside-option return proxies

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