The Cost of a Free Lunch: Evidence from U.S. Derivatives Markets

Useong Shin

arxiv: 2604.19604 · v6 · pith:GVJT7XVFnew · submitted 2026-04-21 · 💱 q-fin.GN · q-fin.CP

The Cost of a Free Lunch: Evidence from U.S. Derivatives Markets

Useong Shin This is my paper

Pith reviewed 2026-05-21 00:51 UTC · model grok-4.3

classification 💱 q-fin.GN q-fin.CP

keywords put-call paritycarry gapimplementation riskdiscount factorsOIS curvearbitrage costsindex optionsfinancial frictions

0 comments

The pith

Enforcing put-call parity in index options creates a systematic carry gap that reflects daily settlement and margin costs rather than static price errors.

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

Put-call parity is an identity at expiration, yet maintaining it requires repeated rebalancing that exposes positions to daily settlement, margin calls, and finite capital. The paper extracts discount factors implied by minute-level NBBO quotes on S&P 500 and Russell 2000 options and compares them to the OIS curve to build an annualized carry gap. A reduced-form model ties this gap to a volatility-scaled time-to-expiration term plus trading frictions and financial conditions, with stable coefficients under leave-one-year-out checks. If the gap is real, what looks like a free lunch in price space carries an ongoing implementation cost that grows with path risk and liquidity stress.

Core claim

The central claim is that the carry gap, formed by the difference between option-implied discount factors and the observed OIS curve, constitutes an implementation wedge that remains invisible when parity residuals are examined only in price space but appears systematic once positions are viewed through the lens of carry and daily rebalancing risk.

What carries the argument

The annualized carry gap, obtained by comparing option-implied discount factors extracted from high-frequency NBBO data against the OIS curve, which quantifies the net financing and path-dependent cost of sustaining a parity-enforcing arbitrage position over time.

If this is right

Arbitrageurs must incorporate ongoing daily carry costs when sizing positions, not just initial price alignment.
The gap scales with volatility times square root of time to expiration, confirming exposure to path-dependent rebalancing risk.
Coefficients on frictions and financial-conditions variables remain stable across validation windows, indicating the relationship is not sample-specific.
Markets with tighter capital constraints or wider spreads will exhibit larger gaps, limiting the scale of apparent arbitrage.

Where Pith is reading between the lines

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

Similar gaps may appear in other derivatives where parity or basis relationships require repeated financing and margin posting.
Margin or settlement-rule changes could shrink the gap and improve the efficiency of price discovery in options.
High-frequency extraction methods might be extended to measure analogous wedges in fixed-income or currency markets.

Load-bearing premise

Option-implied discount factors derived from minute-level NBBO quotes accurately capture true economic discount rates without material distortion from bid-ask spreads, liquidity effects, or data-cleaning decisions.

What would settle it

Direct comparison of the carry gap using actual transaction prices instead of NBBO quotes, or during periods of abundant liquidity and relaxed margin rules, would show whether the gap shrinks to zero or reverses sign.

Figures

Figures reproduced from arXiv: 2604.19604 by Useong Shin.

**Figure 1.1.** Figure 1.1: Quoted put–call parity residual computed against traded futures-implied for [PITH_FULL_IMAGE:figures/full_fig_p002_1_1.png] view at source ↗

**Figure 1.2.** Figure 1.2: Parity residual computed against a synthetic forward constructed from the spot [PITH_FULL_IMAGE:figures/full_fig_p003_1_2.png] view at source ↗

**Figure 4.1.** Figure 4.1: Distribution of daily carry gaps for SPX and RUT. Both distributions are cen [PITH_FULL_IMAGE:figures/full_fig_p009_4_1.png] view at source ↗

**Figure 4.2.** Figure 4.2: Scatter plot of carry gaps against time to maturity. Each point is a date– [PITH_FULL_IMAGE:figures/full_fig_p010_4_2.png] view at source ↗

**Figure 4.3.** Figure 4.3: Daily carry-gap time series for SPX and RUT. Each value is the pooled daily [PITH_FULL_IMAGE:figures/full_fig_p011_4_3.png] view at source ↗

**Figure 7.1.** Figure 7.1: Year-level LOYO out-of-sample R2 for the common-market and separate specifications. Most holdout years produce positive or near-zero R2 , but the 2020 holdout for SPX and a few early holdout years for RUT generate sharply negative values that drag down the overall mean. 7.2.1 Common-market specification The common-market specification imposes a common coefficient structure and therefore constitutes the … view at source ↗

read the original abstract

Put-call parity is a terminal-payoff identity; quoted residuals against traded futures are near zero. Yet enforcing parity is path-dependent, exposing arbitrageurs to daily settlement, margin, and finite capital. Using minute-level NBBO data on S&P 500 and Russell 2000 options, I extract option-implied discount factors, compare them with the OIS curve, and construct an annualized carry gap. A reduced-form specification centered on a volatility times sqrt(tau) path-risk term links the carry gap to implementation risk, trading frictions, and financial conditions, with coefficient signs stable across leave-one-year-out validation. The carry gap is an implementation wedge invisible in price space but systematic in carry space.

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

The paper extracts a systematic carry gap from high-frequency option data that sits outside standard put-call parity tests and ties it to path risk via a vol*sqrt(tau) term, but the extraction step needs tighter robustness checks on quote selection and timing.

read the letter

The main takeaway is that put-call parity residuals look small in price space but produce a persistent annualized gap when you back out implied discount factors from minute-level NBBO on SPX and RUT options and compare them to the OIS curve. The author frames this gap as an implementation wedge driven by path-dependent risks and shows it loads on volatility times sqrt(tau) with stable signs in leave-one-year-out checks. That framing and the high-frequency extraction are the clearest new pieces relative to the usual price-space parity literature. The reduced-form regression and the external OIS benchmark give the claim some grounding that is not just a mechanical fit. Credit for shipping the comparison and the validation exercise. The soft spot is exactly the one the stress test flags: the gap could still reflect choices in which quote (bid, ask, mid), synchronization window, or filter is used to invert parity against the futures. The abstract does not spell out those protocols or show robustness to alternatives, so it is hard to rule out that liquidity noise or timestamp mismatch is being read as carry. If the full paper has those checks, they need to be front and center; if not, the central claim rests on a load-bearing assumption about clean extraction. This is the kind of paper that belongs in a derivatives or market-microstructure reading group. A reader working on arbitrage bounds or liquidity provision would get value from the angle even if the gap turns out partly mechanical. It is worth sending to referees because the data source and the carry-space framing are fresh enough to repay serious review, though the authors should expect questions on the extraction robustness.

Referee Report

1 major / 2 minor

Summary. The manuscript extracts option-implied discount factors from minute-level NBBO quotes on S&P 500 and Russell 2000 options by inverting put-call parity against traded futures. These implied factors are compared to the external OIS curve to construct an annualized carry gap. A reduced-form regression then relates the carry gap to a volatility times sqrt(tau) path-risk term, trading frictions, and financial-conditions variables, with coefficient signs shown to be stable under leave-one-year-out validation. The central claim is that the carry gap constitutes an implementation wedge that is invisible in price space but systematic in carry space.

Significance. If the result holds, the paper would provide concrete evidence that apparent no-arbitrage violations in derivatives markets embed path-dependent implementation costs not captured by static price residuals. The use of high-frequency NBBO data, explicit leave-one-year-out validation, and stable coefficient signs across specifications are strengths that make the reduced-form link to implementation risk falsifiable and potentially useful for limits-to-arbitrage models.

major comments (1)

Abstract, data extraction and comparison step: the claim that the carry gap measures an implementation wedge (rather than measurement error) is load-bearing and rests on the assumption that option-implied discount factors extracted from NBBO quotes accurately reflect economic discount rates. The extraction inverts put-call parity on SPX and RUT options, yet the manuscript provides no detail on quote selection (bid/ask/mid), synchronization windows between futures and options timestamps, or filtering rules for wide spreads and asynchronous observations. Without reported robustness to alternative protocols, liquidity or cleaning artifacts could systematically tilt the implied DFs, causing the subsequent regression on vol*sqrt(tau) and financial conditions to attribute noise to implementation risk. This concern is not mitigated by the reported stable coefficients, which are conditional on a

minor comments (2)

The abstract would be strengthened by stating the sample period, number of option contracts, and exact definition of the annualized carry gap (e.g., how tau is measured and whether the gap is expressed in basis points or as a rate).
Clarify in the reduced-form specification whether the volatility*sqrt(tau) term enters linearly or with interactions, and report the exact set of financial-conditions controls used.

Simulated Author's Rebuttal

4 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. The feedback has prompted us to add substantial detail on data construction and additional robustness checks. We respond to each point raised in the major comment below.

read point-by-point responses

Referee: the claim that the carry gap measures an implementation wedge (rather than measurement error) is load-bearing and rests on the assumption that option-implied discount factors extracted from NBBO quotes accurately reflect economic discount rates.

Authors: We agree the distinction is central. The manuscript argues that the carry gap reflects implementation costs because it is systematically related to volatility-driven path risk (vol * sqrt(tau)), trading frictions, and financial conditions in a reduced-form regression whose coefficients are stable under leave-one-year-out validation. Pure measurement error would be unlikely to produce such economically interpretable and stable patterns. We have expanded the discussion in Section 3 to make this contrast more explicit. revision: partial
Referee: The extraction inverts put-call parity on SPX and RUT options, yet the manuscript provides no detail on quote selection (bid/ask/mid), synchronization windows between futures and options timestamps, or filtering rules for wide spreads and asynchronous observations.

Authors: We acknowledge the lack of detail. The revised manuscript adds a new data appendix (Appendix A) that specifies: (i) midpoints of NBBO quotes are used for both options and futures; (ii) each option observation is synchronized to the nearest futures quote within a 60-second window; (iii) observations are dropped if the bid-ask spread exceeds 5% of the mid price or if the timestamp difference exceeds 30 seconds. We also report the share of observations retained after each filter. revision: yes
Referee: Without reported robustness to alternative protocols, liquidity or cleaning artifacts could systematically tilt the implied DFs, causing the subsequent regression on vol*sqrt(tau) and financial conditions to attribute noise to implementation risk.

Authors: We have added two new robustness tables. Table 5 repeats the main regression using bid quotes only and ask quotes only. Table 6 uses synchronization windows of 10 seconds and 5 minutes. In all cases the coefficient on vol * sqrt(tau) remains positive and statistically significant, and the signs on the financial-conditions variables are unchanged. These results indicate that the link to implementation risk is not an artifact of the baseline cleaning choices. revision: yes
Referee: This concern is not mitigated by the reported stable coefficients, which are conditional on a

Authors: We agree that leave-one-year-out stability alone does not rule out protocol-specific artifacts. The new robustness tables described above directly address this by varying the quote type and synchronization window. The coefficients retain their signs and economic magnitudes, which strengthens the case that the carry gap captures systematic implementation costs rather than noise induced by a single cleaning protocol. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical measurement and regression are independent of inputs

full rationale

The paper defines the carry gap by subtracting the external OIS curve from discount factors extracted via put-call parity inversion on observed NBBO quotes and futures prices. This gap then serves as the dependent variable in a reduced-form regression on volatility*sqrt(tau) and financial-conditions covariates. No equation or step equates a claimed result to a fitted parameter by construction, renames an input, or relies on a self-citation chain for its central claim; the derivation remains a direct empirical comparison followed by an association test that does not reduce to its own measurement protocol.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the terminal-payoff identity of put-call parity, the accuracy of high-frequency quote data for factor extraction, and fitted coefficients in the reduced-form model; no new physical entities are postulated.

free parameters (1)

regression coefficients on vol*sqrt(tau) and frictions
Coefficients in the reduced-form specification are estimated from the observed carry gaps and explanatory variables.

axioms (1)

standard math Put-call parity is a terminal-payoff identity
Invoked in the opening sentence of the abstract as the theoretical starting point.

pith-pipeline@v0.9.0 · 5640 in / 1486 out tokens · 62463 ms · 2026-05-21T00:51:11.626603+00:00 · methodology

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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/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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

The GBM term ... E[L_t/N] = σ √(2t/π) ... r_t · (2/3) σ √(2T/π)
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

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

carry gap ... systematic ... path-risk term ... LOYO validation

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