arxiv: 2604.19604 · v4 · submitted 2026-04-21 · 💱 q-fin.GN · q-fin.CP

Recognition: 2 theorem links

· Lean Theorem

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

Useong Shin

Pith reviewed 2026-05-11 00:43 UTC · model grok-4.3

classification 💱 q-fin.GN q-fin.CP

keywords put-call paritycarry gapimplementation riskoptions arbitrageOIS curvepath-dependent costsderivatives marketsS&P 500 options

0 comments

The pith

Enforcing put-call parity incurs hidden carry costs from daily settlement and margin risks despite near-zero price residuals.

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

The paper demonstrates that put-call parity holds tightly in quoted prices for S&P 500 and Russell 2000 options against futures, yet the act of enforcing it through actual trades exposes arbitrageurs to path-dependent costs including daily settlements, margin requirements, and limited capital. Using minute-level NBBO data, the author extracts option-implied discount factors, compares them to the OIS curve, and builds an annualized carry gap that captures these implementation frictions. A reduced-form regression centered on a volatility times square-root-of-time path-risk term then connects the gap to trading frictions and financial conditions, with coefficients that remain stable under leave-one-year-out checks. If the link holds, what appears as an arbitrage free lunch in price space turns out to be systematically costly in carry space, altering how market efficiency is measured in derivatives.

Core claim

Put-call parity is a terminal-payoff identity with quoted residuals against traded futures near zero, yet enforcing parity is path-dependent and exposes arbitrageurs to daily settlement, margin, and finite capital. Minute-level NBBO data on S&P 500 and Russell 2000 options are used to extract option-implied discount factors, which are compared with the OIS curve to construct an annualized carry gap. A reduced-form specification centered on a volatility times sqrt(tau) path-risk term links this carry gap to implementation risk, trading frictions, and financial conditions, with coefficient signs stable across leave-one-year-out validation. The carry gap therefore functions as an implementation

What carries the argument

The carry gap, defined as the annualized difference between option-implied discount factors and the OIS curve, which measures the systematic wedge between price-space parity and carry-space implementation costs.

If this is right

Arbitrage in options markets is bounded by cumulative path costs rather than static price discrepancies alone.
Market participants must incorporate carry-space metrics when sizing parity trades, not just terminal residuals.
Financial conditions and volatility levels directly scale the effective cost of maintaining parity positions.
Standard no-arbitrage tests that ignore daily settlement frictions understate the true barriers to enforcement.

Where Pith is reading between the lines

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

Similar hidden wedges may appear in other terminal identities such as covered-interest parity once path-dependent margin flows are measured.
High-frequency market makers could reduce but not eliminate the gap if their own capital and settlement constraints scale with volatility.
Regulators monitoring derivatives could add carry-gap series to existing volatility and margin-stress indicators to detect rising implementation friction.

Load-bearing premise

The reduced-form regression centered on the volatility times sqrt(tau) path-risk term correctly isolates implementation risk without omitted-variable bias or post-hoc functional-form choices.

What would settle it

If the carry gap shows no positive correlation with the volatility times sqrt(tau) term in out-of-sample periods or if the regression coefficients flip sign when any single year is dropped from the sample, the claim that the gap reflects path-dependent implementation risk would be refuted.

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 measures a systematic carry gap in put-call parity enforcement for two equity index options markets and links it empirically to a volatility-based path-risk term.

read the letter

The main thing to know is that this paper extracts option-implied discount factors from minute-level NBBO data on S&P 500 and Russell 2000 options, compares them to the OIS curve to build an annualized carry gap, and then runs a reduced-form regression showing that gap correlates with a volatility times sqrt(tau) term plus controls, with stable signs in leave-one-year-out checks. The gap appears in carry space even when price residuals from put-call parity look small. What is new is the specific construction of this annualized gap and its framing as an implementation wedge driven by path-dependent costs like daily settlement and margin. The granular data and the validation exercise are clear strengths; they give the measurement some credibility beyond a simple cross-section. The soft spots are in the regression itself. The central term is reduced-form, so other unmodeled factors such as liquidity premia, funding shocks, or margin dynamics could easily correlate with both the gap and volatility, leaving the attribution to path risk open to question. The paper does not show that the functional form was fixed before looking at the data, which adds a modest post-selection concern. Scope is also narrow—only two indexes—so it is not yet clear how general the pattern is. This is the kind of work that would interest readers focused on limits to arbitrage and microstructure in derivatives markets. It has enough empirical content and internal consistency to merit sending out for peer review, though any referee would likely press on robustness to alternative specifications and omitted variables.

Referee Report

2 major / 2 minor

Summary. The paper extracts option-implied discount factors from minute-level NBBO quotes on S&P 500 and Russell 2000 options, compares them to the OIS curve to construct an annualized carry gap, and estimates a reduced-form regression that attributes variation in this gap to a volatility times sqrt(tau) path-risk term plus controls for frictions and financial conditions. Coefficient signs are reported as stable under leave-one-year-out validation. The central claim is that the carry gap constitutes a systematic implementation wedge invisible in price space but detectable in carry space.

Significance. If the attribution holds, the result would document a previously unmeasured path-dependent cost of enforcing put-call parity in index options markets, with potential implications for arbitrage bounds, margin requirements, and the design of reduced-form pricing models that incorporate implementation risk. The high-frequency data extraction and out-of-sample stability checks are positive features.

major comments (2)

[regression specification / methods] The reduced-form specification centers on a volatility times sqrt(tau) term without an explicit a priori derivation from a structural model of margin or settlement risk. Section describing the regression (or the methods paragraph following the gap construction) should clarify whether this functional form was selected before or after inspecting the data; if post-hoc, the attribution to implementation risk is vulnerable to omitted-variable bias from correlated liquidity or funding factors.
[validation and robustness] Leave-one-year-out validation shows stable signs but does not address functional-form sensitivity or omitted-variable tests. The manuscript should report results under alternative specifications (e.g., linear volatility, log(tau), or interactions with margin requirements) and include a formal test for whether the vol*sqrt(tau) coefficient remains significant after adding proxies for liquidity premia or funding shocks.

minor comments (2)

[data construction] Clarify the exact data filters applied to NBBO quotes (e.g., minimum quote size, time-to-expiration cutoffs, or handling of stale quotes) in the data section.
[gap construction] The abstract refers to 'option-implied discount factors' but the full text should explicitly state the formula used to back out the implied rate from put-call parity residuals.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments, which help clarify the empirical approach and strengthen the robustness section. We respond to each major comment below and indicate planned revisions.

read point-by-point responses

Referee: [regression specification / methods] The reduced-form specification centers on a volatility times sqrt(tau) term without an explicit a priori derivation from a structural model of margin or settlement risk. Section describing the regression (or the methods paragraph following the gap construction) should clarify whether this functional form was selected before or after inspecting the data; if post-hoc, the attribution to implementation risk is vulnerable to omitted-variable bias from correlated liquidity or funding factors.

Authors: The vol × √τ term is motivated by the economic reasoning that path-dependent implementation risks (daily settlement, margin calls) accumulate with the square root of horizon length under standard diffusion assumptions for the underlying price process. This functional form was selected on theoretical grounds prior to full regression estimation. We will revise the methods section to state this motivation explicitly and confirm the ex-ante choice of specification, reducing concerns about post-hoc selection while retaining the reduced-form nature of the analysis. revision: yes
Referee: [validation and robustness] Leave-one-year-out validation shows stable signs but does not address functional-form sensitivity or omitted-variable tests. The manuscript should report results under alternative specifications (e.g., linear volatility, log(tau), or interactions with margin requirements) and include a formal test for whether the vol*sqrt(tau) coefficient remains significant after adding proxies for liquidity premia or funding shocks.

Authors: We agree that expanded robustness analysis is warranted. The revised manuscript will report coefficient estimates under alternative functional forms, including linear volatility, log(τ), and interactions with margin-requirement proxies. We will also estimate an augmented regression that adds proxies for liquidity premia and funding shocks, and we will test and report the statistical significance of the vol × √τ coefficient in that specification. revision: yes

Circularity Check

0 steps flagged

No significant circularity in empirical construction and reduced-form regression

full rationale

The paper measures the carry gap directly from minute-level NBBO data by extracting option-implied discount factors and subtracting the OIS curve, then annualizing the difference. It subsequently estimates a reduced-form regression that associates this independently constructed gap with a volatility times sqrt(tau) term plus controls. No step in the provided abstract or description reduces a claimed result to its inputs by definition, renames a fitted parameter as a prediction, or relies on self-citation for a uniqueness theorem. The functional form is presented as centered on path-risk without evidence that the regression outcome is forced tautologically. This is a standard empirical workflow with separate measurement and testing stages.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the terminal identity of put-call parity (standard in finance) and the validity of extracting discount factors from NBBO quotes; the reduced-form model introduces fitted coefficients whose selection is not detailed in the abstract.

free parameters (1)

coefficients on volatility*sqrt(tau) and other regressors
The reduced-form specification links the carry gap to these terms, implying parameters fitted to the data.

axioms (1)

standard math Put-call parity holds exactly as a terminal-payoff identity
Explicitly stated in the abstract as the starting point.

pith-pipeline@v0.9.0 · 5409 in / 1458 out tokens · 65746 ms · 2026-05-11T00:43:21.922383+00:00 · methodology

Review history (2 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.Cost.FunctionalEquation washburn_uniqueness_aczel unclear
The GBM term used in this paper translates this structure into basis points... GBM_OIS,1Y_i,t = 10^4 * OIS_1Y_t/100 * 2/3 * Vol_i,t/100 * sqrt(2 tau_i,t / pi)
IndisputableMonolith.Foundation.RealityFromDistinction reality_from_one_distinction unclear
A reduced-form specification centered on a volatility times sqrt(tau) path-risk term links the carry gap to implementation risk

Reference graph

Works this paper leans on

12 extracted references · 9 canonical work pages

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