Annualized Settlement Wedge (ASW)

Updated 5 July 2026

Annualized Settlement Wedge (ASW) is an annualized measure capturing the discount in near-certain claims due to delayed settlement and locked capital.
In prediction markets, ASW emerges from frontier-implied settlement discounts, while in index derivatives it is mirrored by the carry gap between OIS and option-implied discount factors.
Empirical evidence shows ASW varies with maturity and market frictions such as daily settlement, variation margin, and funding pressures, highlighting its role as a practical indicator of settlement risk.

Searching arXiv for the specified papers and closely related ASW terminology to ground the article in current literature. (searching arXiv) Annualized Settlement Wedge (ASW) denotes an annualized compensation term embedded in prices when a claim is economically close to certain or statically replicable but settlement, redeemability, or enforcement is delayed. In collateralized prediction markets, ASW is defined from a frontier-implied settlement discount and measures the required return on capital locked in unresolved positions (Gebele et al., 29 May 2026). In U.S. index-derivatives markets, a closely related object appears as the carry gap or implementation wedge: the annualized log difference between the OIS discount factor and the option-implied discount factor recovered from put–call parity (Shin, 21 Apr 2026). In both settings, the wedge is not a terminal-payoff contradiction; it is a carry-space or settlement-space adjustment generated by path dependence, daily settlement, variation margin, funding pressure, illiquidity, and finite arbitrage capital.

1. Formal definitions and scope

In prediction markets, the reduced-form pricing equation is

$P_{i,t}=\mathbb{E}_{t}[X_i]\cdot D(\tau_{i,t}),$

where $X_i\in\{0,1\}$ is the contract payoff, $P_{i,t}$ is the market price, $\tau_{i,t}$ is remaining time until settlement or redeemability, and $D(\tau)\in(0,1]$ is the settlement discount factor. The paper parameterizes

$D(\tau)=\exp\!\bigl(-r_{\mathrm{PM}}\tau\bigr),$

with $r_{\mathrm{PM}}$ interpreted as the required return on capital locked in unresolved prediction-market positions. From a near-certainty frontier price $P_q(\tau)$ , the implied continuously compounded rate is

$r_q(\tau)=-\frac{1}{\tau}\log P_q(\tau),$

and the Annualized Settlement Wedge is

$\mathrm{ASW}_q(\tau)=\exp\!\bigl(365\,r_q(\tau)\bigr)-1.$

The paper therefore treats ASW as an annualized implied yield or carry rate on a near-certain claim that is delayed rather than immediately redeemable (Gebele et al., 29 May 2026).

In the index-options setting, the central object is termed the carry gap rather than ASW. Put–call parity is written as

$X_i\in\{0,1\}$ 0

with the synthetic forward

$X_i\in\{0,1\}$ 1

Using the strike cross-section at a given maturity, the paper estimates $X_i\in\{0,1\}$ 2 and defines the carry gap as

$X_i\in\{0,1\}$ 3

with basis-point version

$X_i\in\{0,1\}$ 4

The paper states that, in the sense relevant here, this carry gap is essentially the same object as an annualized settlement wedge: a wedge between an option-implied discount structure and a benchmark discount structure, annualized by dividing the log discount-factor gap by time to maturity, and tied economically to settlement, margin, and capital frictions rather than terminal-payoff mispricing (Shin, 21 Apr 2026).

Setting	Core object	Annualization
Prediction markets	Frontier-implied settlement discount $X_i\in\{0,1\}$ 5	$X_i\in\{0,1\}$ 6
Index options	OIS vs. option-implied discount factor gap	$X_i\in\{0,1\}$ 7

This scope distinction is important. ASW is explicit in the prediction-market literature, whereas in derivatives the same economic content is framed as a carry gap or implementation wedge.

2. Economic mechanism: delayed dollars and path-dependent enforcement

The prediction-market interpretation begins from the claim that a collateralized prediction-market price is not only a belief about event probability; it is a discounted expected payoff. Even if the outcome is economically obvious, the winning claim may remain formally unsettled, non-redeemable, collateral-locked, exposed to residual oracle or platform risk, and unable to earn outside returns. On Polymarket, the paper emphasizes that resolution runs through UMA’s Optimistic Oracle, so there is a delay between the real-world event becoming effectively determined and the moment the winning claim becomes redeemable. In that setting, a near-certain dollar is a delayed dollar, and ASW measures the compensation required for waiting (Gebele et al., 29 May 2026).

The derivatives interpretation starts from a different institutional mechanism but reaches a closely related conclusion. Put–call parity is exact as a terminal-payoff identity, yet enforcing parity requires a path-dependent trade. A position can be riskless at maturity while still being exposed before maturity to interim mark-to-market losses, daily settlement or variation margin, capital calls, liquidation risk, and nonsynchronous execution. The paper formalizes normalized interim P&L as

$X_i\in\{0,1\}$ 8

and introduces the minimal support capital process $X_i\in\{0,1\}$ 9 satisfying

$P_{i,t}$ 0

with

$P_{i,t}$ 1

Using Brownian-motion properties, expected support capital scales as

$P_{i,t}$ 2

and average capital commitment over the life of the trade is

$P_{i,t}$ 3

The resulting path-risk object is proportional to $P_{i,t}$ 4, so the cost of keeping the arbitrage alive grows with volatility and horizon (Shin, 21 Apr 2026).

Taken together, these mechanisms imply that ASW is not fundamentally a claim about misbelief or quoted mispricing. It is a reduced-form price of delayed redeemability, locked capital, or required support capital. This suggests that the wedge is endogenous to market infrastructure and balance-sheet constraints rather than being a purely statistical artifact.

3. Identification and empirical construction

The prediction-market paper recovers the settlement-discount term structure from persistent near-certain contracts. The identifying sample uses markets where one side is persistently $P_{i,t}$ 5 for seven consecutive daily snapshots, with exclusions for markets showing large reversals. The logic is that when one side stays in the upper tail for multiple days, and especially when the event is economically resolved but still unsettled, the remaining gap to par is mostly settlement discount rather than belief uncertainty. The paper writes

$P_{i,t}$ 6

so that

$P_{i,t}$ 7

Because residual uncertainty and discounting are observationally confounded, the paper estimates a high-quantile frontier $P_{i,t}$ 8 at each horizon, using minimum, $P_{i,t}$ 9-percentile, and $\tau_{i,t}$ 0-percentile frontiers. Realized settlement time, proxied by realized closeDate or oracle-finalization timing, is used as the relevant horizon variable, and the paper notes that standard non-differential measurement error in realized settlement times implies attenuation toward zero rather than mechanically creating a positive horizon gradient. The workflow then converts frontier prices to implied rates, annualizes them into ASW, and tracks time variation through a daily minimum-frontier object $\tau_{i,t}$ 1. The paper also computes $\tau_{i,t}$ 2 as a concentration diagnostic for the low-APY frontier-support tail (Gebele et al., 29 May 2026).

The derivatives paper operationalizes its analogue from minute-level NBBO option quotes on SPX and RUT from ThetaData, restricted to European-style index options to avoid early-exercise complications. For each date and maturity, calls and puts with the same strike are paired; the synthetic-forward identity is applied across the full strike cross-section rather than at a single at-the-money point; low-liquidity and noisy observations are filtered out; and date–maturity cells with unreliable OIS recovery are excluded. The cross-sectional fit yields $\tau_{i,t}$ 3, which is then compared with the bootstrapped OIS discount factor. Daily values are aggregated as the median across eligible minute-level observations, producing a date-by-maturity panel of annualized carry gaps for SPX and RUT and then a daily market-level series (Shin, 21 Apr 2026).

The two identification strategies differ in implementation but are structurally similar. Each isolates a discount term from a setting in which the raw price object can appear nearly efficient: near-certain contracts that remain below par, or option prices that satisfy parity in price space while generating a systematic gap in carry space.

4. Empirical regularities in prediction-market ASW

The prediction-market paper reports that ASW is positive, maturity-dependent, and time-varying. The baseline term structure is positive throughout, falls sharply at the short end, stabilizes by roughly 20 days, and then rises again at long horizons with a hump around 230–260 days. The short end is partly constrained by CLOB tick size: a $\tau_{i,t}$ 4 ask and $\tau_{i,t}$ 5 bid imply a midpoint of $\tau_{i,t}$ 6, so very small discounts at short maturities can annualize into very large ASWs. Over calendar time, the frontier-implied ASW is higher earlier in the sample and compresses later; early observations show high lower-tail ASWs and concentrated frontier support, while late 2024 onward shows compressed frontier rates and broader support (Gebele et al., 29 May 2026).

A central empirical result is that discount adjustment materially reduces the observed maturity gradient in pricing errors. The raw tail regression

$\tau_{i,t}$ 7

produces

$\tau_{i,t}$ 8

After discount adjustment using

$\tau_{i,t}$ 9

the estimated slopes fall to $D(\tau)\in(0,1]$ 0 under the minimum-ASW frontier, $D(\tau)\in(0,1]$ 1 under the $D(\tau)\in(0,1]$ 2-percentile frontier, and $D(\tau)\in(0,1]$ 3 under the $D(\tau)\in(0,1]$ 4-percentile frontier, corresponding to reductions of $D(\tau)\in(0,1]$ 5, $D(\tau)\in(0,1]$ 6, and $D(\tau)\in(0,1]$ 7, respectively. Under the $D(\tau)\in(0,1]$ 8-percentile frontier, the residual slope is statistically indistinguishable from zero. Event-level 5-fold cross-fitting yields held-out-event slope reductions of $D(\tau)\in(0,1]$ 9 to $D(\tau)=\exp\!\bigl(-r_{\mathrm{PM}}\tau\bigr),$ 0. The paper summarizes this as a $D(\tau)=\exp\!\bigl(-r_{\mathrm{PM}}\tau\bigr),$ 1– $D(\tau)=\exp\!\bigl(-r_{\mathrm{PM}}\tau\bigr),$ 2 attenuation of the near-certainty horizon gradient (Gebele et al., 29 May 2026).

The paper also compares ASW descriptively with AAVE lending yields and 2-year Treasury yields. It finds overall correlation with AAVE around $D(\tau)=\exp\!\bigl(-r_{\mathrm{PM}}\tau\bigr),$ 3, pre-election positive co-movement for some horizons, weaker linkage after the election, and weak Treasury correlations. These comparisons are presented as descriptive benchmarks rather than direct arbitrage relations. The broader implication is that a substantial portion of the raw horizon gradient in near-certainty contracts can reflect priced settlement frictions rather than forecast error alone.

5. Carry gap as an ASW analogue in U.S. derivatives markets

The derivatives paper’s main empirical claim is that quoted parity residuals against traded futures are near zero, yet the annualized carry object extracted from parity is systematically positive. In the full sample, the daily carry gap distribution has mean $D(\tau)=\exp\!\bigl(-r_{\mathrm{PM}}\tau\bigr),$ 4 bp, median $D(\tau)=\exp\!\bigl(-r_{\mathrm{PM}}\tau\bigr),$ 5 bp, and $D(\tau)=\exp\!\bigl(-r_{\mathrm{PM}}\tau\bigr),$ 6 positive observations. By market, SPX has mean $D(\tau)=\exp\!\bigl(-r_{\mathrm{PM}}\tau\bigr),$ 7 bp and median $D(\tau)=\exp\!\bigl(-r_{\mathrm{PM}}\tau\bigr),$ 8 bp, while RUT has mean $D(\tau)=\exp\!\bigl(-r_{\mathrm{PM}}\tau\bigr),$ 9 bp and median $r_{\mathrm{PM}}$ 0 bp. The level is fairly flat across maturities, roughly $r_{\mathrm{PM}}$ 1– $r_{\mathrm{PM}}$ 2 bp, but dispersion is much larger at short maturities, a pattern the paper attributes to the $r_{\mathrm{PM}}$ 3 annualization and to microstructure frictions such as nonsynchronicity and illiquidity. The time series is elevated in 2018, elevated again in 2020–2021, lower in 2022–2023, and rebounding in 2024–2025 (Shin, 21 Apr 2026).

To relate this wedge to implementation risk, the paper estimates a reduced-form specification centered on a GBM-derived path-risk term scaled by short and long interest rates. The construction uses VIX for SPX and RVX for RUT and interprets the resulting regressor as the opportunity cost of capital committed to an arbitrage position exposed to path risk. The baseline pooled regression includes $r_{\mathrm{PM}}$ 4, $r_{\mathrm{PM}}$ 5, median bid–ask spread scaled by maturity, and NFCI. The estimated coefficients are negative for $r_{\mathrm{PM}}$ 6, about $r_{\mathrm{PM}}$ 7, positive for $r_{\mathrm{PM}}$ 8, about $r_{\mathrm{PM}}$ 9, positive for $P_q(\tau)$ 0, about $P_q(\tau)$ 1, and negative for NFCI, about $P_q(\tau)$ 2, all highly significant. Across leave-one-year-out validation, the signs are stable in 10 out of 10 years (Shin, 21 Apr 2026).

The paper interprets the negative short-rate coefficient as mechanical compression of the annualized carry gap when short-term rates rise and the short-end discount factor moves quickly. The positive long-rate coefficient is read as a long-run capital opportunity-cost channel: when long-term yields are high, capital is more valuable elsewhere, so arbitrageurs are less willing to commit balance sheet to parity enforcement, widening the wedge. The positive bid–ask coefficient indicates that trading frictions widen the wedge. The negative NFCI coefficient is interpreted more cautiously as part of the state dependence of arbitrage capital and implementation pressure rather than a standalone causal mechanism.

This evidence is central to the broader ASW concept because it shows how a wedge can be invisible in quoted price residuals yet systematic once translated into annualized carry space. The core message is not that put–call parity fails at expiration, but that the capital burden of enforcing it along the path is priced.

6. Market design, interpretation, and adjacent concepts

The prediction-market paper emphasizes that market architecture changes ASW. In negRisk markets, conversion compresses the wedge by recycling part of the position into synthetic collateral. The paper proves the payoff identity

$P_q(\tau)$ 3

so a NO basket can be decomposed into a deterministic cash-like component plus only the residual complementary YES exposure. For the canonical $P_q(\tau)$ 4 case, the average NO price is approximately

$P_q(\tau)$ 5

The paper finds that negRisk markets stay closer to par than non-negRisk markets, that within negRisk larger outcome sets lie even closer to par, that the ordering is clearest at medium and long horizons, and that all series converge toward par near maturity. It also derives fee-adjusted versions in which conversion fees and taker fees raise the effective wedge, especially at short horizons. A second design channel is collateral yield: comparing Polymarket with Kalshi, the paper reports that Kalshi’s frontier stays closer to par and flatter across maturities, interpreting this as consistent with yield-bearing collateral reducing the effective settlement discount, while noting that this is a cross-platform comparative static rather than a clean causal treatment effect (Gebele et al., 29 May 2026).

These results address two common misconceptions. First, in collateralized prediction markets, price below 1 need not imply a corresponding lack of certainty about the outcome; it may reflect delayed redeemability and locked capital. Second, in options markets, near-zero quoted parity residuals do not imply the absence of a systematic funding wedge; the wedge can be nearly invisible in price space and still persistent in carry space. In both cases, price does not map one-to-one into an immediately realizable payoff.

A related but distinct issue appears in “Is the annualized compounded return of Medallion over 35%?” (Guo et al., 2024). That paper does not use the term ASW explicitly. Its closest analogue is the claim that naïvely compounding reported yearly returns is incorrect when fund value is discontinuous and cash flows or profit allocations break standard compounding logic. The corrected size-profit methodology yields an annualized compounded return of $P_q(\tau)$ 6 before fees, while a manager-wealth proxy yields $P_q(\tau)$ 7, leading the authors to conclude that Medallion’s annualized compounded return is probably under $P_q(\tau)$ 8 (Guo et al., 2024). This suggests a broader methodological theme: annualized objects can be materially distorted when observed prices or returns abstract from settlement timing, capital lock-up, or discontinuous reinvestment paths.

Within the current literature, ASW therefore denotes more than a narrow anomaly statistic. It is a reduced-form measure of the cost of waiting for a payoff that is near-certain or terminally pinned down, but not immediately accessible. Its empirical content depends on how the underlying market settles, how collateral is treated, how capital can be recycled, and how much path-dependent support is required to keep an ostensibly riskless position alive.