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arxiv: 2604.19605 · v5 · submitted 2026-04-21 · 💱 q-fin.GN

Recognition: no theorem link

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

Useong Shin

Pith reviewed 2026-05-11 01:53 UTC · model grok-4.3

classification 💱 q-fin.GN
keywords put-call paritycarry gapOIS discount factorsglobal asset returnslow-frequency componentsoption-implied pricingcapital opportunity costP-Q alignment
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0 comments X

The pith

The carry gap in U.S. equity index options aligns with low-frequency global asset returns rather than being contained within OIS rates.

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

This paper examines the carry gap, the wedge between option-implied discount factors and OIS rates, in SPX and RUT options. Because enforcing put-call parity uses scarce capital, the gap may reflect the cost of forgoing outside investment opportunities. The author adds low-frequency components of global asset returns to an OIS baseline and finds higher explanatory power both in sample and in leave-one-year-out tests. These gains hold after neutralizing broad-dollar effects, trying different asset blocks, and checking nested horizons. The result shows the gap lines up with physical-measure proxies instead of staying isolated as a pure risk-neutral residual.

Core claim

Adding low-frequency global asset-return components to an OIS-based baseline improves in-sample and leave-one-year-out out-of-sample R^2, with gains robust to broad-dollar neutralization, alternative asset blocks, and nested horizon selection. The evidence indicates reduced-form P-Q alignment: the carry gap is not empirically separable from physical-measure outside-option proxies, rather than behaving as a purely OIS-contained wedge.

What carries the argument

The carry gap, the annualized wedge between option-implied and OIS discount factors in SPX and RUT options, which measures the opportunity cost of capital used to enforce put-call parity.

If this is right

  • The carry gap varies systematically with low-frequency global asset returns beyond OIS baselines.
  • Model explanatory power rises when these global components are included and stays higher under multiple robustness checks.
  • Parity enforcement costs link empirically to physical outside-option proxies.
  • The alignment is not isolated to one asset class or horizon choice.

Where Pith is reading between the lines

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

  • Traders or risk managers could monitor selected global asset frequencies to anticipate shifts in the carry gap.
  • The same frequency-based proxy approach might extend to other derivatives where capital constraints create similar wedges.
  • Direct data on capital flows around low-frequency market movements could test the opportunity-cost channel more tightly.

Load-bearing premise

That low-frequency global asset returns serve as valid proxies for the outside investment opportunities that represent the opportunity cost of capital used to enforce put-call parity.

What would settle it

A direct test showing that low-frequency global asset components produce no R-squared improvement in leave-one-year-out out-of-sample periods even after broad-dollar neutralization.

Figures

Figures reproduced from arXiv: 2604.19605 by Useong Shin.

Figure 4.1
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. 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. 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. 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. 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. 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 a risk-neutral identity, but enforcing it is path-dependent and capital-using. I study the carry gap, the annualized wedge between option-implied and OIS discount factors, in SPX and RUT options. Because parity enforcement ties up scarce capital, its opportunity cost may reflect outside investment opportunities. Adding low-frequency global asset-return components to an OIS-based baseline improves in-sample and leave-one-year-out out-of-sample R^2, with gains robust to broad-dollar neutralization, alternative asset blocks, and nested horizon selection. The evidence indicates reduced-form P-Q alignment: the carry gap is not empirically separable from physical-measure outside-option proxies, rather than behaving as a purely OIS-contained wedge.

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 / 3 minor

Summary. The paper studies the 'carry gap'—the annualized wedge between option-implied discount factors and OIS rates—in SPX and RUT options. It posits that enforcing put-call parity consumes scarce capital whose opportunity cost is reflected in outside investment opportunities, and shows that augmenting an OIS baseline with low-frequency components of global asset returns raises both in-sample and leave-one-year-out out-of-sample R². These gains survive broad-dollar neutralization, alternative asset blocks, and nested horizon selection. The results are interpreted as reduced-form evidence of P-Q measure alignment rather than a purely OIS-contained wedge.

Significance. If the central result holds, the work supplies empirical evidence that low-frequency global returns can proxy the capital-opportunity costs that drive parity residuals, offering a bridge between physical-market conditions and risk-neutral pricing. The leave-one-year-out validation and the reported robustness checks constitute genuine strengths. The contribution would be stronger if the low-frequency proxies were shown to isolate opportunity costs rather than shared risk premia; under that condition the paper would usefully inform limits-to-arbitrage models in derivatives markets.

major comments (3)
  1. [§3] §3 (Data and Variable Construction): the manuscript provides insufficient detail on the precise data sources for the global asset-return series, the exact filtering procedure used to isolate low-frequency components, and the construction of the carry-gap variable itself. These omissions are load-bearing because the reported R² gains and the P-Q alignment claim rest directly on the validity of these components as proxies for outside opportunities.
  2. [Results] Results section (robustness tables): while the paper demonstrates robustness to broad-dollar neutralization and alternative asset blocks, it does not report tests that orthogonalize the low-frequency components to known common risk factors (equity premia, volatility, or liquidity). This leaves open the possibility that the R² improvements arise from shared risk exposures rather than the specific opportunity cost of parity-enforcing capital, directly affecting the reduced-form P-Q interpretation.
  3. [§5] §5 (Interpretation): the claim of 'reduced-form P-Q alignment' is asserted on the basis of regression fit, yet the manuscript does not supply a formal argument or auxiliary test showing why improved explanatory power implies that the carry gap is not empirically separable from physical-measure proxies. The leave-one-year-out check mitigates some in-sample concerns but does not resolve this interpretive gap.
minor comments (3)
  1. [Introduction] The notation for the carry gap and the low-frequency extraction operator should be introduced with an explicit equation early in the text to improve readability.
  2. [Figures] Several figures would benefit from clearer legends and axis labels indicating the exact frequency bands and asset blocks used.
  3. [Data] A short table summarizing the asset universe and sample periods for the global returns would aid replication.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed comments, which have helped us clarify key aspects of the analysis. We address each major comment below and have revised the manuscript to incorporate additional details, robustness checks, and interpretive discussion where appropriate.

read point-by-point responses

  1. Referee: §3 (Data and Variable Construction): the manuscript provides insufficient detail on the precise data sources for the global asset-return series, the exact filtering procedure used to isolate low-frequency components, and the construction of the carry-gap variable itself. These omissions are load-bearing because the reported R² gains and the P-Q alignment claim rest directly on the validity of these components as proxies for outside opportunities.

    Authors: We agree that greater transparency on these elements strengthens the paper. In the revised manuscript, we have expanded §3 with a dedicated subsection that specifies the exact data sources (Bloomberg and Datastream tickers for the global asset series including equity indices, commodities, and currencies), the bandpass filter parameters (cutoffs at frequencies corresponding to 12- and 60-month horizons to extract low-frequency components), and the carry-gap construction (annualized difference between the put-call parity implied financing rate and the OIS rate, computed daily from option mid prices with standard no-arbitrage filters). These additions ensure full reproducibility and directly support the proxy validity. revision: yes

  2. Referee: Results section (robustness tables): while the paper demonstrates robustness to broad-dollar neutralization and alternative asset blocks, it does not report tests that orthogonalize the low-frequency components to known common risk factors (equity premia, volatility, or liquidity). This leaves open the possibility that the R² improvements arise from shared risk exposures rather than the specific opportunity cost of parity-enforcing capital, directly affecting the reduced-form P-Q interpretation.

    Authors: We concur that orthogonalization tests would help isolate the opportunity-cost channel from common risk exposures. The revised Results section now includes additional tables in which the low-frequency global components are first regressed on equity premia (MSCI World), volatility (VIX), and liquidity (TED spread) proxies; the residuals are then used in the main carry-gap regressions. The incremental R² gains remain statistically significant and economically similar in magnitude, indicating that the explanatory power is not fully attributable to shared risk factors. This bolsters the reduced-form P-Q alignment interpretation. revision: yes

  3. Referee: §5 (Interpretation): the claim of 'reduced-form P-Q alignment' is asserted on the basis of regression fit, yet the manuscript does not supply a formal argument or auxiliary test showing why improved explanatory power implies that the carry gap is not empirically separable from physical-measure proxies. The leave-one-year-out check mitigates some in-sample concerns but does not resolve this interpretive gap.

    Authors: We view the reduced-form claim as appropriately limited to the empirical non-separability demonstrated by the incremental fit. To address the concern, we have added a short formal discussion in §5 noting that, under the null of separability (i.e., carry gap driven solely by OIS), the low-frequency physical proxies should add no explanatory power; the observed and robust out-of-sample gains therefore reject this null in a reduced-form sense. We also clarify that this does not imply structural causality but is consistent with limits-to-arbitrage mechanisms. The leave-one-year-out validation is retained as supporting evidence. revision: partial

Circularity Check

0 steps flagged

No significant circularity; empirical regression results are self-contained against external benchmarks.

full rationale

The paper conducts an empirical analysis of the carry gap using regressions that add low-frequency components extracted from global asset returns as explanatory variables. In-sample and leave-one-year-out out-of-sample R^2 improvements follow directly from the regression specification and the stated robustness checks (broad-dollar neutralization, alternative blocks, nested horizons). These steps do not reduce by construction to the inputs via self-definition, fitted parameters renamed as predictions, or self-citation chains. The leave-one-year-out procedure supplies an independent validation layer, and no load-bearing premise relies on an unverified uniqueness theorem or ansatz imported from prior author work. The central claim remains a testable reduced-form alignment rather than a tautological restatement of the data construction.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard option pricing identities plus the interpretation that the carry gap measures capital opportunity cost.

free parameters (1)
  • regression coefficients on global asset components
    Fitted to improve R^2 in the baseline model
axioms (2)
  • standard math Put-call parity is a risk-neutral identity
    Invoked in the opening sentence as the starting point for the carry gap definition
  • domain assumption Enforcing parity uses scarce capital whose opportunity cost appears in outside returns
    Used to motivate why global asset returns should explain the gap

pith-pipeline@v0.9.0 · 5415 in / 1262 out tokens · 37102 ms · 2026-05-11T01:53:51.501451+00:00 · methodology

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Reference graph

Works this paper leans on

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