Notes on non-stationarity in crypto perpetual funding

Funding rates on perpetual swaps get presented, in most explainers and most trading-desk decks, as a simple anchor. The perp drifts from spot, funding kicks in, longs pay shorts or the other way round, and the price gets pulled back into line. Mechanical, thermostatic even. It is the kind of description that survives because it is true often enough to feel like a law.

Spend any real time staring at funding series across venues, though, and the law stops holding. The anchor starts to look less like a thermostat and more like a pressure gauge on a system with several independent things pushing on it at once. The number printed every interval is a noisy reflection of a balance constantly being renegotiated: aggregate inventory sitting on market makers’ books, leverage demand from directional traders who could not care less about basis, and venue-specific schedules and caps that differ exchange to exchange for no principled reason. Treat that reading as a clean, stable signal and you will build something that works beautifully on the data you tuned it on and loses money quietly once it meets data it has not seen.

The mechanics, briefly

The funding mechanism exists to keep a perpetual future, which has no expiry and therefore no natural convergence to spot, roughly tracking the underlying anyway. Every interval, commonly eight hours though some venues run hourly, the exchange compares the perp’s price to a spot or index reference and pays the gap from one side of the book to the other.

If the perp trades above the index, funding is usually positive and longs pay shorts; below it, shorts pay longs. A trader holding a leveraged long through a period of persistently positive funding pays a running fee, deducted from margin at the end of each interval regardless of whether the position is working. Hold that long through enough eight-hour windows and the carry cost stops being a footnote and starts eating the trade.

That is the whole mechanism. What makes it interesting is not the formula, which is public and simple, but the input to it: the aggregate behaviour of every participant on the venue, and that is neither public nor simple.

What actually drives the number

Pull the driver apart and three forces are doing most of the work, and they do not sit still relative to each other.

Market-maker inventory is the quiet one. Makers mostly try to run flat, and when directional flow leaves them holding a lopsided position they lean on their quotes to shed it: the standard inventory-risk response, skewing whichever side of the quote reduces the pile fastest. I will not assert a clean, one-line causal path from a given skew to the sign of the premium, since that depends on venue marks and hedging practice, and getting the direction wrong quietly breaks a model built on it. What seems clear is that inventory skew mostly follows the move instead of causing it: it shifts because leverage demand, described next, shifted first.

Leverage demand from directional traders is the loud one, and it is where the mechanism’s actual stabilising force lives. When retail sentiment turns euphoric, everyone wants the same leveraged long at once, and that crowd bids the perp above spot on its own, no market maker required. The resulting premium pushes funding positive, so the crowd of longs is now paying the crowd of shorts to hold that view. The more crowded the trade, the more it costs to stay in it, which is meant to thin the crowd back out. It is not a fast lever: a rich enough conviction will happily keep paying for days or weeks before the fee changes anyone’s mind.

Then there is venue structure, the part people underweight most. Every exchange sets its own funding interval, its own index calculation, and often a rate cap that clips the number well before it reaches whatever the raw imbalance implies. A venue with an eight-hour interval and a generous cap expresses the same imbalance quite differently to one running hourly with a tight cap. Cross-venue funding arbitrage exists precisely because these mechanical differences do not net out. Two numbers both labelled “funding rate,” pulled from two venues, come out of two different rulebooks measuring a similar but not identical thing, and treating them as one time series is where naive cross-venue analysis quietly goes wrong.

None of these three moves in isolation. A venue’s cap binds hardest in exactly the moments when directional demand is most extreme, which is also when cross-venue arbitrage looks most attractive, feeding back into inventory everywhere else at once. Skew, demand and caps behave as coupled components of one system rather than independent inputs, and the coupling changes strength depending on what the market is doing.

Why stationarity fails

The naive approach, tempting because it is so easy to implement, is to treat the funding rate as a single stationary mean-reverting process. Fit an Ornstein-Uhlenbeck-style model to the whole history, estimate a single mean, reversion speed and volatility for the lot, and trade deviations from that fitted mean. The backtest looks wonderful, because most of history spent most of its time in one or two dominant regimes, and a model fitted to a mixture quietly dominated by one component will describe that component well and call it a day.

The trouble shows up live, because regime shifts in funding sit closer to the median experience than to a rare edge case. Variance changes with broader risk sentiment: funding sits calm and tight in a grinding, low-volume market and swings violently during a liquidation cascade, when leveraged longs get force-closed en masse and the imbalance pushes the rate somewhere the calm-period model never priced as plausible. Autocorrelation changes too. In a trending market funding can stay persistently elevated for weeks, refusing to revert on any horizon the calm-period model would call reasonable, then snap back over a single day once the trend breaks. Structural breaks compound both: a venue changes its interval or tightens its cap, its participant mix shifts as a rival product launches and pulls volume away, and the process you were modelling has quietly become a different process wearing the same ticker.

I keep coming back to a comparison from outside finance entirely: a weather forecaster whose model trained on one very calm, very dry summer. It will produce excellent forecasts for more of that same summer, having learned the one regime it was shown in exhaustive detail. Point it at the first autumn storm front and it will not just be a little off, it will be confidently wrong in a way that looks, from the inside, exactly like being right, because nothing in its training ever told it a different kind of day was possible. A funding model trained through a single calm regime fails the same way: not by producing visibly bad numbers but by producing entirely plausible ones that describe a world which has already stopped existing. How you would even detect that kind of failure before it costs you money deserves a longer note of its own, but I want to keep this one anchored to funding and not wander off into general model-monitoring territory.

Conditioning, and what it costs

What we have found, and I want to be careful about how strong a claim this is, is that even crude regime conditioning measurably improves things. Bucket by realised volatility over a trailing window. Bucket by a recent funding-z-score against its own short history. Fit separate distributional parameters within each bucket instead of one set across everything. Against a single unconditional model, the conditioned version holds up noticeably better out-of-sample, and degrades more gracefully when a regime it has seen before recurs.

The cost is not subtle. Every extra bucket is a smaller sample feeding each fit, and funding history, by the standards a systematic trader works with, is short. It is the ordinary bias-variance tradeoff in a funding-market costume: conditioning cuts the bias from pretending one distribution covers every regime, bought at the price of higher estimation variance, since each bucket now has less data behind it, a real trade with a real cost attached. Get the bucketing too fine and you are fitting noise with a straight face. Get it too coarse and you have bought a marginally more expensive single-distribution model and called it regime awareness.

Open questions

We do not have closed-form answers here. Three questions keep coming back around when we discuss this internally.

How much of what looks like non-stationarity is structural, venue rules and participant mix genuinely changing under our feet, versus a sampling artefact from histories too short to have shown us the full range of one stable process? We suspect it is a mix and do not yet have a clean way to separate the two.

Are there leading indicators of a regime transition that do not already bleed straight through into spot volatility, which would make them redundant with something we are already watching? If funding regime shifts are just a lagging shadow of spot vol ones, conditioning on funding history buys us less than it looks like it does.

And what is the right horizon for calling something “stationary enough” to model as one distribution? A day, a week, a handful of funding intervals? The answer probably depends on the venue and the instrument. That is an unsatisfying place to land, though it is honestly where the evidence has us right now. We will pick up specific pieces of this in later notes rather than try to close the whole thing out here.