The Bitcoin Yield Curve
What it costs to borrow against Bitcoin, at every tenor, discovered by competitive auction and settled on-chain. No price oracle sits in the chain, and no formula sets the rate — every point is a loan someone actually agreed to.
The current term structure
| Tenor | Rate (APR) |
|---|---|
| 7 days | 6.16% · model |
| 14 days | 5.66% |
| 30 days | 5.32% |
| 60 days | 5.21% |
| 90 days | 5.24% |
| 180 days | 5.42% |
| 365 days | 5.80% |
| 730 days | 6.36% · model |
Fitted from 15 active loans across 6 tenor bins. 24 auctions have cleared in total. Active loans are what the curve is made of; an auction that cleared and a loan since repaid are different counts, and only the first is in this fit.
Log-quadratic fit through bin means, R² 0.33 — measured against those bin means, so at low counts it reports how smooth the bins are, not how good the fit is.
15 observations from 2 counterparties, 0 external.
Observations are currently predominantly own-account. Aletheia Analytics participates on own account to seed observable auction data. This is not yet an independent market assessment.
Tenors marked model have no auction in their bin: the fit defines a rate there, but nothing was observed at that maturity. A tenor with no fitted rate at all shows as not yet discovered.
This curve is published as ASCR-BTC
The Bitcoin rate has a name, a permanent methodology URL and a revision policy: ASCR-BTC, an instance of the Auction-Settled Credit Rate (ASCR) family. Cite it, chart it or republish it freely, with attribution — there is no licence to negotiate.
How the curve is built
A borrower posts Bitcoin (WBTC) as collateral and describes the loan they want: an amount in USDC, a duration, and the most they are willing to repay. Lenders then compete in an open auction, bidding the rate down. The auction closes, the loan settles on-chain, and that settlement is one point: a real rate, at a real tenor, that two parties actually agreed to.
Collect enough of those points and you have a term structure. The canonical curve bins the active loans into standard tenors and fits a log-quadratic through the bin means — rate = β₀ + β₁·ln(d) + β₂·ln(d)² — which captures normal, inverted and humped shapes naturally in log-duration space. Tenors with no bin beneath them are marked as model output rather than passed off as observations.
No oracle, no algorithm, no committee
Every other rate in crypto credit is set by a formula. Utilisation-curve protocols compute the rate from how much of a pool is borrowed — a parameter chosen by governance, not a price discovered by anyone. Oracle-dependent protocols import an external price feed and liquidate against it, which makes the feed itself a risk. Neither produces a term structure, because neither has terms: the rate floats and the loan has no maturity.
Gavel has fixed terms and no oracle in the loan lifecycle. The rate comes from competitive bidding, and the loan runs to maturity without a price feed to trigger against. That is what makes a curve possible here and not elsewhere: there are discrete maturities, and the rate at each one was discovered rather than computed.
What this curve is not
It is not deep. It currently rests on 15 active loans, from 24 auctions cleared to date. A benchmark earns its authority from volume and continuity, and this one is early. Treat it as what it is: the honest output of a young market, published as it stands.
It is not a risk-free rate, despite the temptation to read it as one. It is the rate at which over-collateralised Bitcoin credit cleared, including whatever the market prices for smart-contract risk, collateral volatility and the borrower's option to walk away. It is not a quote, not an offer, and not a rate you can transact at by reading this page — it is a record of what already happened.
Where a tenor shows no rate, the market has not discovered it. We do not interpolate across gaps or extend the curve past the longest settled loan.
Every point is a transaction
The curve is derived, not asserted. The auctions behind it settle on Arbitrum and are verifiable independently of anything on this page — the protocol is permissionless and open-source, and the contracts are public. The same data is available over the API and to AI agents over the Model Context Protocol.
Informational purposes only — not financial advice or a recommendation. Rates shown are historical records of settled auctions, not offers.