Keep the Carry, Hedge the Tail: Funding-Rate Options for Perpetual Futures

1. Introduction

Perpetual futures are a foundational instrument in digital-asset markets. Unlike dated futures, perpetuals never expire and lack natural convergence to spot prices. Exchanges instead use recurring funding payments to align perpetual and spot markets: longs pay shorts when positive, and shorts pay longs when negative [1]. In 2025, the ten largest centralized perpetual exchanges processed $86.2 trillion in volume, with decentralized venues adding $6.7 trillion [2]. Funding-rate exposure is thus embedded in digital assets’ largest risk-transfer channel, directly affecting directional traders, basis traders, market makers, protocol treasuries, and synthetic-dollar issuers [3]–[5].

Ethena exemplifies why this exposure matters independently of directional price risk. The protocol issues the synthetic dollar USDe ($4.1 billion circulating as of September 1, 2026 [6]) and hedges backing collateral with short perpetuals. While delta-neutral, this structure retains perpetual funding cash flows. Ethena explicitly identifies prolonged negative funding as a threat to yield and backing, relying on an internal reserve fund to absorb negative-revenue periods [7]. Beyond synthetic dollars, any perpetual position decouples price risk from recurring funding risk. Because delta-neutral short positions motivate our study, we analyze negative funding as the adverse event; the symmetric long-side formulation follows directly by sign inversion.

Market participants currently manage funding risk by accumulating reserves, trimming positions, diversifying across venues, or executing fixed-for-floating swaps. For example, Boros exchanges floating funding for a fixed annualized rate [4], [8]. Yet each approach involves substantial trade-offs:

• Reserves absorb losses internally without transferring risk.
• Position reduction sacrifices balance-sheet scale and yield.
• Venue diversification fails during market-wide funding stress.
• Swaps surrender positive carry by fixing floating rates symmetrically.

Hedgers often prefer asymmetric protection: contracts that retain positive carry while insuring against severe, persistent, or cumulative adverse draws.

Existing literature on perpetual futures primarily studies contract mechanics and asset pricing. Angeris et al. [9] examine model-free funding rates and static replication. He et al. [3] establish no-arbitrage bounds and document perpetual-to-spot basis deviations. Ackerer, Hugonnier, and Jermann [10] derive dynamic replication prices across linear, inverse, and quanto perpetuals. Kim and Park [11] analyze funding mechanisms for price convergence. These works explain how perpetuals are priced and anchored, but do not treat realized adverse funding cash flows as a separable, insurable loss process.

Our contribution is not the invention of deductibles, stop-loss claims, or tail-risk metrics [12], [13], but their actuarial adaptation to perpetual funding and integration into an empirical hedge-selection framework: the FROST (Funding-Rate Options for Selective Tail-risk transfer) architecture. Fig. 1 illustrates this foundational mechanism: decoupling floating carry from catastrophic tail drawdowns.

We investigate three core questions:

1. Empirical Loss Dynamics: How does adverse perpetual-funding risk accumulate over time, and to what extent does temporal clustering amplify tail severity?
2. Contingent Contract Design: How can option-style claims be structured and valued actuarially to transfer adverse draws while preserving positive carry?
3. Risk-Constrained Selection: Which hedge minimizes total economic cost across varying degrees of risk tolerance, and how sensitive is this choice to the underwriter’s valuation rule?

2. The FROST Framework: Contract Design, Actuarial Valuation, and Hedge Selection

The primary dataset contains 7,971 eight-hour Bybit funding observations from November 15, 2018, to February 23, 2026. Excluding non-standard settlement timestamps yields 7,634 regular rolling 30-day windows (n = 90 eight-hour intervals), our benchmark horizon for evaluating hedges. Let 𝒯 = {1, . . . , n} denote the index set of intervals and τ = 30/365 its annualized fraction.

Let denote the funding cash flow per unit of short-perpetual exposure in interval t, where fₜ > 0 is received funding and fₜ < 0 is paid funding. To isolate adverse cash flows requiring reserve liquidity, we define

where x⁺ = max(x, 0). Here ℓₜ is the adverse payment in interval t and Λ is the cumulative adverse draw over the 30-day horizon. Crucially, the cumulative metric Λ excludes favorable carry offsets, measuring the exact liquidity drain that a treasury must reserve against.

A. Existing benchmarks and proposed hedge designs

We compare two existing responses to funding risk with three contingent contracts. The first benchmark is self-insurance: the user buys no protection and retains the entire adverse draw,

The second benchmark is an interest rate swap. A swap replaces a chosen fraction of the future floating funding stream with a fixed rate agreed at the beginning of the horizon. If h ∈ [0, 1] is the fraction hedged and s is the fixed rate, the resulting funding cash flow in interval t becomes

Here h = 0 leaves funding completely floating, while h = 1 fixes the entire funding stream. The corresponding adverse funding draw is

Lacking continuous historical swap quotes, we evaluate two backward-looking benchmark policies using information available prior to each window: a 90-interval arithmetic mean and a 90-interval exponential average (45-interval half-life). The hedge-selection procedure selects freely between them.

An interest rate swap stabilizes the entire funding stream. The three contracts we introduce instead transfer only selected adverse states while leaving favorable funding unchanged.

Table I summarizes our three FROST contract designs. The Interval Floor reimburses individual adverse payments exceeding deductible d. The Distress-Activated Floor (DAF) conditions payouts on persistence: rₜ counts consecutive intervals below distress threshold −b, with coverage starting only once rₜ ≥ m (with m = 3, intervals 3–5 of a 5-interval episode are covered, without retroactive reimbursement for intervals 1–2). The Aggregate Stop-Loss (ASL) abstracts from trajectory, reimbursing cumulative adverse draw Λ exceeding attachment D.

For options, h ∈ [0, 1] denotes the insured fraction of underlying exposure, yielding residual adverse draw:

Here h = 1 delivers full notional protection, while h = 0.5 covers half. Because Π℗ ≤ Λ, residual draw satisfies X℗(h) ≥ 0 for all h ≤ 1. For swaps, h denotes the fraction of floating funding converted to fixed.

B. Calibrating the contracts

To prevent lookahead bias and model overfitting, the principal contract parameters are calibrated strictly from the historical funding distribution prior to pricing:

The baseline Interval Floor establishes a deductible of one basis point (d = 0.0001) per eight-hour interval, which lies just above the median adverse funding payment conditional on a negative observation and filters approximately 58% of the smallest adverse intervals; the buyer therefore retains frequent minor payments while transferring severity beyond this baseline. The baseline DAF establishes matching severity (b = d = 0.0001) and persistence (m = 3) thresholds: the severity threshold b isolates distress intervals, while the persistence parameter m = 3 restricts coverage until adverse funding endures for three consecutive intervals (24 hours). Setting b = d ensures that payouts approach zero continuously as funding approaches the threshold.

For the ASL, the attachment is linked directly to the distribution of 30-day cumulative adverse funding. We calibrate D = q₉₀(Λ) as the baseline attachment and D = q₉₉(Λ) as a deeper tail layer. These choices deliberately place coverage around the worst 10% and 5% of historical 30-day adverse-funding draws. Their corresponding in-sample activation frequencies are therefore direct consequences of the calibration rule rather than independent metrics of performance.

C. Pricing contracts that do not yet trade

Comparing unlisted contingent claims requires an economically consistent pricing benchmark. Our baseline actuarial quote prices expected claims, tail-risk exposure, and seller capital commitments:

where τ = 30/365, λ = 0.35 is the tail-risk loading, kₛ = 12% is the seller’s annual capital opportunity cost, and CVaR⁺₁% is the average of the worst 1% of claims.

Because underwriter pricing is a modeling choice, we evaluate three alternative valuation rules (holding payoffs and buyer metrics fixed): expected-value pricing, Wang probability distortion (θ = 0.5) [14], and target-Sharpe pricing (S* = 0.75), detailed in Appendix A. This sensitivity establishes which conclusions are robust to the underwriter’s pricing framework.

D. Comparing the hedges

We evaluate each hedge by asking two questions: how much adverse funding risk remains, and what does the protection cost? For each strategy j and hedge ratio h, let X℗(h) denote the residual adverse funding draw defined above. Our principal risk measure is

the average residual draw in the worst 1% of 30-day windows. This measure is deliberately more demanding than asking only for the loss threshold at the 99th percentile, as it also captures the severity of outcomes beyond that threshold.

The buyer also bears a cost for obtaining protection. We define the 30-day funding-risk-management cost as

where A℗(h) is direct hedge expenditure, K℗(h) is capital committed to residual funding risk or hedge margin, τ = 30/365, and the baseline buyer opportunity cost is k₉ = 10%. The seller and buyer capital rates need not coincide because they represent the opportunity costs of different balance sheets. For an option,

while self-insurance uses A₀ = 0 and K₀ = R₀. Because option payouts reduce the retained draw X℗(h), this accounting treats expected claims symmetrically. Specifically, the expected-claim component of the premium is offset by the corresponding reduction in expected retained loss, isolating the seller’s loading and residual capital requirement as the true incremental cost of risk transfer.

For the historical swap benchmarks, Aₛ𝒶𝃚𝑝(h) = 0 because the fixed-rate cash flows are already included directly in Xₛ𝒶𝃚𝑝(h). When reserve and margin can be supported by the same collateral pool, we define the fixed-leg margin proxy and capital requirement jointly as:

An additive treatment is retained as a sensitivity.

As a supporting diagnostic for the option designs, we also calculate reserve-risk reduction per unit of premium,

A high value means that each unit of premium removes a relatively large amount of worst-case reserve exposure. This indicates how efficiently an option transfers tail risk, but it does not by itself determine the final hedge choice.

The final decision rule incorporates both risk and cost. Suppose a user specifies a maximum acceptable residual tail loss R̄. We discard hedges that cannot meet this limit and choose the least costly strategy that remains:

Evaluating Equation (17) across tighter risk limits R̄ generates the Risk-Constrained Hedge-Selection Map in Section III. Because the contract set is discrete and h is one-dimensional, we solve (17) by exact grid enumeration across h ∈ {0.00, 0.01, . . . , 1.00}, recomputing residual draws, CVaR, capital charges, and total cost at every point. Infeasible strategies (R℗(h) > R̄) are discarded, and the minimum-cost feasible hedge is selected. Reported ratios are exact grid optima.

After constructing the baseline comparison, we test which conclusions depend on its assumptions. We reprice the option payoffs under the alternative seller-pricing rules described above, examine historical-era subsamples, repeat the option-efficiency analysis at 7- and 90-day horizons, and use dependent block resampling to assess sampling uncertainty while preserving short-run dependence. Data from Binance, BitMEX, and Deribit substantiate the empirical portability of funding tail parameters across distinct exchange architectures, as evaluated in Section III.

3. Empirical Results

Negative funding occurs in 18.4% of the Bybit observations, but these intervals are not evenly scattered through time. Conditional on a negative interval, the probability of an immediately subsequent negative payment rises to approximately 50.5%, demonstrating that adverse funding clusters into persistent, multi-day episodes.

These episodes become economically severe when accumulated over the 30-day horizon. Across the 7,634 regular windows,

of notional. The median is only approximately 0.077%. The 99th-percentile adverse draw is therefore roughly 37 times the median.

Fig. 2A shows that cumulative adverse funding has a long right tail, while Panel B shows that the level of that tail changes substantially through time. The trailing two-year q₉₉ ranges from approximately 0.15% to 2.28% of notional across the available estimation periods. We can precisely define contract payoffs even when the historical loss distributions used to value them depend strongly on market regimes.

Table II substantiates the empirical portability of these contract specifications across four major centralized derivatives venues. Bybit and Binance display remarkably consistent baseline dynamics, sharing an identical median annualized funding rate (10.95%), comparable negative interval frequencies (18.4% vs. 17.7%), and nearly identical median 30-day cumulative losses (≈ 0.078%). This confirms that the baseline deductible d = 1 bp and DAF persistence condition m = 3 transfer seamlessly across standard centralized venues. In contrast, Deribit features a distinct microstructure without a fixed 1-bp interest rate baseline, resulting in a lower median APR (1.52%) and smaller median cumulative draw (0.024%), yet its unconstrained rate mechanism produces extreme right-tail losses (q₉₉ = 2.728%), requiring proportionally scaled attachments. BitMEX spans earlier market regimes with higher retail leverage, yielding elevated episode frequency (54.3%) and wider dispersion (q₉₉ = 7.528%). Thus, while the qualitative superiority of contingent tail protection holds universally, underwriter attachment thresholds must be calibrated to venue-specific microstructure.

How the contracts reshape funding risk

The contracts trade breadth of protection against selectivity. The Floor covers severe individual payments regardless of what happens elsewhere in the month. The DAF avoids paying for isolated observations, but consequently leaves the beginning of persistent episodes and all shorter episodes with the buyer. The ASL instead ignores the sequence of payments and concentrates protection on months in which cumulative adverse funding becomes large.

Under the baseline 30-day pricing rule, the ASL variants remove approximately 2.66–2.70 units of tail reserve per unit of premium, compared with approximately 2.31–2.45 for the evaluated Floor and DAF variants. The ASL family also remains highest-ranked under the option-efficiency metric when the contracts are repriced under the retained alternative premium rules and when the comparison is repeated at additional horizons. Absolute prices vary materially across these specifications, but the relative efficiency of aggregate-tail protection is more stable.

The baseline DAF is never selected by the risk-constrained map, and the m = 2 sensitivity does not change the selected families.

Risk-constrained hedge-selection map

Without protection, the average adverse draw in the worst 1% of 30-day windows is approximately R₀ = 3.745% of notional. We then ask how the preferred hedge changes as a user demands progressively lower residual risk.

Fig. 3A first applies the baseline seller quote. Panel B then asks whether the identity of the selected option survives alternative ways of valuing the same payoff distributions.

Table III reports the exact grid optima across all evaluated risk limits, with the minimum-cost feasible strategy boldfaced.

The strongest distinction is between the moderate and stringent risk regions. At the R̄ = 2.00% target, the partial mean-policy swap is far cheaper than any option. Once the risk limit is tightened below the range attainable by the historical swap benchmarks, contingent protection becomes necessary. At the R̄ = 0.75% target the Interval Floor is the only tested family capable of satisfying the constraint, and no tested strategy reaches R̄ = 0.50%.

The intermediate option ranking is less universal. Under the baseline CVaR-loaded quote, the Interval Floor is cheaper than the best ASL by only 1.6 basis points at R̄ = 1.50% and 0.9 basis points at R̄ = 1.00%. Pure expected-value pricing also selects the Floor, by approximately 0.2 basis points. Wang and target-Sharpe pricing reverse the ranking and select an ASL. Thus the robust result is not a universal ordering among Floor and ASL, but a transition from inexpensive partial fixed-rate stabilization to an option-only region in which the preferred contract depends on how the seller prices risk. This sensitivity is primarily a valuation effect rather than an artifact of one historical subperiod, as under the baseline pricing rule, the Interval Floor is least costly in 25 of 26 rolling three-year eras at both intermediate targets.

Moderate protection: partial fixed-rate hedging

At the R̄ = 2.00% residual-risk target, the trailing-mean interest rate swap is the least costly feasible strategy, with half of the floating funding stream converted to fixed under the baseline reserve-risk cost. Approximately 15.9% of historical windows begin with a negative mean-policy fixed-rate estimate, so complete conversion can itself lock an adverse funding rate. Indeed, full conversion does not satisfy the R̄ = 2.00% target under this historical policy, while the EWMA benchmark fails to reach the target at any tested hedge ratio. The preference for a partial mean-policy swap is not solely an artifact of ignoring favorable funding. A separate net-funding sensitivity that explicitly charges the hedge for foregone positive carry still selects the partial mean-policy swap over every option at the R̄ = 2.00% target. These results apply to backward-looking historical benchmark rates, though market-implied forward rates may produce different hedge ratios or feasibility limits.

Aggregate Stop-Loss: efficient tail transfer and a hard cap

The ASL is not a pricing-rule-independent minimum-cost hedge at the intermediate limits. Under the baseline quote it is a close runner-up to the Floor, while Wang and target-Sharpe pricing select the ASL instead. It nevertheless remains the strongest option under the premium-efficiency metric because its payments are concentrated directly on large cumulative-loss windows rather than spread across severe individual observations. At full coverage, the ASL has a useful structural property:

The buyer never retains cumulative adverse funding exceeding the attachment D. For example, if D = 1% of notional, a month with a 0.6% adverse draw leaves the buyer with the full 0.6% loss, while a month with a 3% adverse draw leaves the buyer with only a 1% loss and the ASL pays the remaining 2%.

Because the q₉₀ and q₉₉ attachments are exceeded in more than 1% of historical windows, the average retained loss in the worst 1% also equals D at full coverage:

The retained-loss ceiling is therefore created by the contract itself rather than by an assumption about how severe the tail becomes beyond D. The premium required to provide that protection remains uncertain, but the full-coverage loss cap does not. The hedge-selection map does not generally choose full coverage. When h < 1, the buyer still retains part of every loss above D. For Λ > D,

For example, at h = 0.94 the buyer retains the attachment plus 6% of any loss above it. Partial ASL protection therefore compresses the tail substantially without creating the exact hard ceiling obtained at h = 1.

Broad protection: the Interval Floor

Under the baseline seller quote, the Interval Floor achieves the lowest modeled total cost at all three option-only targets: h = 0.68 at R̄ = 1.50%, h = 0.84 at R̄ = 1.00%, and h = 0.92 at R̄ = 0.75%. Its coverage is broader than the ASL’s because it pays whenever an individual adverse observation exceeds the per-interval deductible rather than waiting for cumulative loss to pass an aggregate attachment. This breadth gives the Floor a larger expected claim and lower reserve reduction per unit of gross premium than the ASL. In the buyer-cost measure, however, expected insurance claims are also reimbursements that reduce retained adverse funding, rather than an additional economic loss. Under the baseline quote, the Floor can therefore meet a given tail constraint with less notional coverage and edges below the ASL on total modeled cost. That advantage is small at the R̄ = 1.00% and R̄ = 1.50% targets and reverses under the Wang and target-Sharpe pricing rules, so it should not be interpreted as structural dominance.

Persistence filters: the Distress-Activated Floor

The core design lesson from the Distress-Activated Floor is that its waiting period excludes the wrong cash flows: the unhedged opening ticks of clustered episodes that still enter CVaR⁺₁%. Although the 50.5% continuation probability of adverse intervals intuitively motivates a persistence requirement, the deductible-style delay leaks the clustered start of those same episodes. Premium falls, but residual tail risk does not. Consequently, persistence filters belong in the contract suite only if the excluded mass is body risk rather than tail risk; a more selective trigger is valuable only when the excluded losses are unimportant to the risk the buyer wants to remove.

These numerical thresholds reflect historical Bybit distributions; forward-implied regimes will scale absolute costs proportionally while preserving the structural ranking between linear and contingent hedges. The tested historical swap policies deliver inexpensive moderate protection but cannot reach the tighter limits. Contingent options extend the feasible risk range, with the Interval Floor uniquely reaching the R̄ = 0.75% target. Within the intermediate option-only region, the least-cost choice depends on the premium rule rather than admitting a universal ranking. Separately, the ASL yields the highest reserve reduction per premium dollar and a contractual retained-loss ceiling at full coverage. Hedge selection therefore depends not only on how much risk a user wants to remove, but also on which economic property of the hedge the user values.

4. Conclusion

We analyze perpetual funding as a separable, one-sided risk process distinct from directional price volatility. Across 7.3 years of Bitcoin perpetual-funding data, adverse funding exhibits persistent temporal clustering and extreme positive skewness, generating severe cumulative draws across 30-day horizons. To transfer this risk while preserving positive carry, we design three contingent option contracts: the Interval Floor, the Distress-Activated Floor, and the Aggregate Stop-Loss.

Our empirical findings demonstrate that no single contract dominates across all risk preferences. For moderate protection (R̄ ≥ 2.00%), partial trailing-mean swaps provide the most economical solution due to zero option-risk loadings. At tighter limits (R̄ ≤ 1.50%), however, linear swap policies become strictly infeasible, requiring option-style protection. Within the intermediate option-only region, contract ranking is sensitive to underwriter valuation: capital-loaded pricing selects the Interval Floor, whereas probability-distorted pricing selects the Aggregate Stop-Loss. Crucially, the Aggregate Stop-Loss achieves the highest tail-risk reduction per premium dollar across all tested pricing regimes and, at full coverage, establishes an absolute contractual ceiling on retained loss. The DAF’s persistence condition fails to provide a compensating efficiency benefit and is never selected.

These results provide a foundational blueprint for on-chain risk transfer. A mature perpetual-futures ecosystem need not constrain participants to an all-or-nothing choice between retaining unhedged floating variance and locking in fixed rates. By employing asymmetric contingent claims, market participants can maintain their exposure to positive carry while immunizing their balance sheets against catastrophic tail risk.

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Appendix A: Alternative Seller-Pricing Rules

The baseline seller quote is defined in Section II-C. To test whether hedge selection depends on that particular valuation rule, we hold each contract payoff distribution fixed and replace only its premium.

Pure expected-value pricing sets

For the Wang sensitivity [14] with distortion parameter θ = 0.5, let Sℿ(x) = Pr(Π > x) denote the payoff survival function and let Φ(·) denote the standard-normal cumulative distribution function. The Wang transform is

giving the distorted premium

The target-Sharpe sensitivity sets target Sharpe ratio S* = 0.75, choosing a premium whose loading relative to payoff volatility equals S*:

Only the option premium changes across these sensitivities; contract payoffs, residual-loss calculations, capital requirements, and the hedge-ratio grid remain fixed.

Paper: Keep the Carry, Hedge the Tail: Funding-Rate Options for Perpetual Futures Track: Open Track Competition: Ledger N3XT Research Competition, 2026

I confirm that this submission is an original research paper produced for the Ledger N3XT Research Competition (Open Track). All empirical analyses, contract formulations, and risk-constrained optimization frameworks presented are original work, with all academic literature, historical market data sources, and industry protocols cited in full academic accordance.

This manuscript is free from plagiarism and has not been published or submitted concurrently to any other conference, journal, or competition. I assume full responsibility for the research, methodology, and conclusions presented.

Gaurav Dev  ·  September 2026

Exotic Structures Pricing Group, TUM Blockchain Club