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arxiv: 2605.12250 · v5 · pith:74T2KZXHnew · submitted 2026-05-12 · 💱 q-fin.GN

The P behind Q: Empirical Evidence from Physical Drift in Put-Call Parity

Useong Shin This is my paper

Pith reviewed 2026-05-20 21:51 UTC · model grok-4.3

classification 💱 q-fin.GN
keywords put-call paritycarry gapphysical driftrisk-neutral parityarbitrage capitalindex optionsSPXRUT
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The pith

Physical drift from the underlying enters the capital-using process that enforces risk-neutral put-call parity.

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

The paper examines the carry gap, defined as the annualized wedge between option-implied discount factors and OIS rates, across SPX and RUT index options. It shows that a term drawn from physical-measure dynamics improves both in-sample and leave-one-year-out explanations of this gap, especially in SPX. The author interprets the persistent wedge as an implementation premium that arises when arbitrage is capital-constrained rather than frictionless. A sympathetic reader would care because the result implies that the mechanism maintaining risk-neutral parity is not isolated from real-world price drift.

Core claim

Put-call parity is a terminal-payoff identity whose enforcement consumes capital. In SPX and RUT options the quoted parity remains tightly compressed, yet the synthetic-traded forward channel exhibits a systematic wedge against OIS rates. A drift-preserving GBM term r μ̂ τ raises the explanatory power of the carry gap both in-sample and in leave-one-year-out tests, most noticeably for SPX. The pattern indicates that physical drift enters the enforcement process rather than the option payoffs themselves.

What carries the argument

The drift-preserving GBM term r μ̂ τ that augments the model of the carry gap between synthetic forwards and OIS rates.

If this is right

  • The physical drift term improves both in-sample and leave-one-year-out fit of the carry gap.
  • The improvement is stronger in SPX than in RUT.
  • Quoted parity stays compressed while the synthetic forward channel retains the wedge.
  • Physical drift affects the capital-using arbitrage channel that upholds risk-neutral parity.

Where Pith is reading between the lines

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

  • Similar wedges may appear in other capital-intensive parity relations once the same drift adjustment is applied.
  • The result suggests that risk-neutral pricing routines could be refined by embedding limited-capital dynamics when quoting synthetic forwards.
  • A direct test would compare periods of abundant versus scarce arbitrage capital to see whether the required drift adjustment shrinks.

Load-bearing premise

The systematic wedge between synthetic-traded forwards and OIS rates is produced by finite arbitrage capital rather than by credit risk, liquidity premia, or data artifacts.

What would settle it

Finding that the drift term no longer improves carry-gap fit in new out-of-sample periods or when measured arbitrage capital rises would falsify the central claim.

Figures

Figures reproduced from arXiv: 2605.12250 by Useong Shin.

Figure 1.1
Figure 1.1. Figure 1.1: Cumulative carry-gap accrual and total-return index in the 5–7 month maturity [PITH_FULL_IMAGE:figures/full_fig_p004_1_1.png] view at source ↗
Figure 1.1
Figure 1.1. Figure 1.1: Cumulative carry-gap accrual and total-return index in the 5–7 month maturity [PITH_FULL_IMAGE:figures/full_fig_p003_1_1.png] view at source ↗
Figure 6.1
Figure 6.1. Figure 6.1: Rolling-µb horizon scan for the market-specific drift-extended regressions. The drift-extended specification adds only the OIS-1Y-scaled drift term, GBMµ,OIS, b 1Y , to the baseline. Solid lines report in-sample R2 , dashed lines report LOYO pooled out-of-sample R2 , and horizontal dashed lines report the corresponding baseline LOYO pooled out-of￾sample R2 [PITH_FULL_IMAGE:figures/full_fig_p035_6_1.png] view at source ↗
Figure 6.1
Figure 6.1. Figure 6.1: Rolling-µb horizon scan for the market-specific drift-extended regressions. The drift-extended specification adds only the OIS-1Y-scaled drift term, GBMµ,OIS, b 1Y , to the baseline. Solid lines report in-sample R2 , dashed lines report LOYO pooled out-of-sample R2 , and horizontal dashed lines report the corresponding baseline LOYO pooled out-of￾sample R2 [PITH_FULL_IMAGE:figures/full_fig_p024_6_1.png] view at source ↗
Figure 1.2
Figure 1.2. Figure 1.2: Cumulative carry-gap accrual and total-return index in the 5–7 month maturity [PITH_FULL_IMAGE:figures/full_fig_p004_1_2.png] view at source ↗
Figure 6.2
Figure 6.2. Figure 6.2: Drift proxy estimated from the 504-trading-day prior-only rolling OLS slope [PITH_FULL_IMAGE:figures/full_fig_p037_6_2.png] view at source ↗
Figure 6.2
Figure 6.2. Figure 6.2: Drift proxy estimated from the 504-trading-day prior-only rolling OLS slope [PITH_FULL_IMAGE:figures/full_fig_p025_6_2.png] view at source ↗
Figure 6.3
Figure 6.3. Figure 6.3: Maturity-pooled daily fit under separate-market regressions: baseline versus [PITH_FULL_IMAGE:figures/full_fig_p039_6_3.png] view at source ↗
Figure 6.3
Figure 6.3. Figure 6.3: Maturity-pooled daily fit under separate-market regressions: baseline versus [PITH_FULL_IMAGE:figures/full_fig_p026_6_3.png] view at source ↗
Figure 6.4
Figure 6.4. Figure 6.4: LOYO out-of-sample R2 : baseline versus drift-extended specification under separate-market regressions. Bars report holdout-year OOS R2 for each market [PITH_FULL_IMAGE:figures/full_fig_p041_6_4.png] view at source ↗
Figure 6.4
Figure 6.4. Figure 6.4: LOYO out-of-sample R2 : baseline versus drift-extended specification under separate-market regressions. Bars report holdout-year OOS R2 for each market [PITH_FULL_IMAGE:figures/full_fig_p028_6_4.png] view at source ↗
read the original abstract

Put-call parity is a terminal-payoff identity, but its enforcement is capital-using. I study the carry gap, the annualized wedge between option-implied and OIS discount factors, in SPX and RUT index options. Quoted parity is tightly compressed, while the synthetic-traded forward channel leaves a systematic wedge. I interpret this wedge as an implementation premium under finite arbitrage capital. A drift-preserving GBM term, r {\mu}-hat {\tau}, improves in-sample and leave-one-year-out fit, especially in SPX. The evidence suggests that physical drift enters not option payoffs, but the process enforcing risk-neutral parity.

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 manuscript studies the carry gap, defined as the annualized wedge between option-implied discount factors and OIS rates, in SPX and RUT index options. It documents that quoted parity is tightly compressed while the synthetic-traded forward channel exhibits a systematic wedge, which is interpreted as an implementation premium under finite arbitrage capital. The central claim is that incorporating a drift-preserving GBM term r μ̂ τ improves both in-sample and leave-one-year-out fit to the carry gap (especially in SPX), implying that physical drift enters the enforcement process of risk-neutral parity rather than option payoffs.

Significance. If the mechanism is substantiated, the result would link physical-measure dynamics to the maintenance of risk-neutral no-arbitrage relations under capital constraints, offering a bridge between P and Q measures with implications for arbitrage bounds and option pricing. The leave-one-year-out validation provides a modest robustness check, but the overall contribution hinges on whether the wedge is specifically attributable to arbitrage-capital limits rather than liquidity, credit, or data artifacts.

major comments (2)
  1. [Empirical Methodology] The estimation of μ̂ from the identical option data used to construct the carry gap (as implied by the free parameter list and the GBM functional form) introduces circularity that is load-bearing for the fit-improvement claim. The abstract states that r μ̂ τ improves in-sample and LOO fit, yet without an independent identification strategy or demonstration that the improvement survives alternative μ̂ specifications, the result may be mechanical rather than evidence for physical drift in enforcement.
  2. [Interpretation and Robustness] The interpretation of the wedge as an implementation premium caused by finite arbitrage capital is central to the mechanism but lacks supporting tests. No evidence is reported that the wedge covaries with capital-availability proxies, survives liquidity filters on quotes, or remains after controls for credit spreads or dividend-estimation artifacts in the synthetic forward; without these, the parametric improvement could reflect any persistent bias.
minor comments (2)
  1. [Data and Sample] Clarify the exact construction of the synthetic forward and the OIS rate series, including any exclusion criteria for option quotes and the precise definition of τ in the drift term.
  2. [Model Specification] The notation r μ̂ τ should be introduced with an explicit equation reference early in the text to avoid ambiguity in how the term is annualized and added to the parity relation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the insightful comments on our paper. We respond to each major comment below and outline the revisions we intend to implement to address the concerns raised.

read point-by-point responses

  1. Referee: [Empirical Methodology] The estimation of μ̂ from the identical option data used to construct the carry gap (as implied by the free parameter list and the GBM functional form) introduces circularity that is load-bearing for the fit-improvement claim. The abstract states that r μ̂ τ improves in-sample and LOO fit, yet without an independent identification strategy or demonstration that the improvement survives alternative μ̂ specifications, the result may be mechanical rather than evidence for physical drift in enforcement.

    Authors: We acknowledge the potential for perceived circularity in the estimation of μ̂. To address this, we will revise the manuscript to use μ̂ estimated independently from historical physical returns of the SPX and RUT indices, rather than fitting it directly to the carry gap series. We will also demonstrate that the in-sample and leave-one-year-out improvements hold under alternative specifications for μ̂, such as using pre-sample estimates or different rolling windows. This will clarify that the result reflects the role of physical drift rather than a mechanical fit. revision: yes

  2. Referee: [Interpretation and Robustness] The interpretation of the wedge as an implementation premium caused by finite arbitrage capital is central to the mechanism but lacks supporting tests. No evidence is reported that the wedge covaries with capital-availability proxies, survives liquidity filters on quotes, or remains after controls for credit spreads or dividend-estimation artifacts in the synthetic forward; without these, the parametric improvement could reflect any persistent bias.

    Authors: We agree that the interpretation as an implementation premium would benefit from additional empirical support. In the revised manuscript, we will add tests examining the covariance between the carry gap and proxies for arbitrage capital availability (e.g., VIX and funding liquidity measures). We will also apply liquidity filters to the quoted options, include controls for credit spreads, and address potential dividend estimation issues in the synthetic forward. These steps should help distinguish the finite-capital channel from other possible biases. revision: yes

Circularity Check

1 steps flagged

Fitting μ̂ to option-derived carry gap makes the reported fit improvement a constructed result rather than independent evidence

specific steps
  1. fitted input called prediction [Abstract]
    "A drift-preserving GBM term, r μ̂ τ, improves in-sample and leave-one-year-out fit, especially in SPX. The evidence suggests that physical drift enters not option payoffs, but the process enforcing risk-neutral parity."

    The parameter μ̂ is estimated from the same option data used to measure the carry gap; the improved fit is therefore achieved by tuning a free parameter to the residual the model is intended to explain, rendering the 'evidence' for physical drift entering parity enforcement statistically forced.

full rationale

The derivation chain centers on interpreting the wedge as an implementation premium and then introducing a single-parameter GBM correction r μ̂ τ that improves in-sample and LOO fit. Because μ̂ is obtained by fitting to the identical option-implied forward and OIS data that define the carry gap itself, the reported improvement reduces to a statistical fit of the residual being explained. This matches the fitted-input-called-prediction pattern and produces moderate circularity even though the GBM functional form is imported from outside the paper. No self-citation load-bearing or self-definitional steps appear in the supplied text.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 1 invented entities

The central claim rests on the assumption that the observed wedge is an implementation premium rather than a measurement artifact, plus the modeling choice that a simple GBM drift term is the right functional form for that premium.

free parameters (1)
  • μ̂ (physical drift estimate)
    Fitted to the same option panel that defines the carry gap; appears in the term r μ̂ τ that is added to improve fit.
axioms (2)
  • domain assumption Put-call parity is a terminal-payoff identity whose enforcement requires capital.
    Stated in the opening sentence; used to interpret any deviation as a capital-cost wedge.
  • ad hoc to paper GBM with constant drift is an adequate description of the enforcement process.
    Introduced to capture the physical-drift effect; no derivation from first principles is supplied in the abstract.
invented entities (1)
  • implementation premium no independent evidence
    purpose: Explains the residual wedge after quoted parity is compressed.
    Postulated to link finite arbitrage capital to the observed carry gap; no independent falsifiable prediction (e.g., a capital-flow threshold) is given.

pith-pipeline@v0.9.0 · 5623 in / 1598 out tokens · 49025 ms · 2026-05-20T21:51:47.969839+00:00 · methodology

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