Borrowing and rates

Credit in a market is sized by a stressed sale and priced by how well first-loss capital covers it. Two formulas set how much a position may borrow and what it pays.

Borrow admission

Public borrowing is judged on a shadow curve: a constant-product tail rebuilt at the pessimistic price and scaled to conservative depth.

$$\hat p = \min(p_{\text{symEMA}}, p_{\text{dirEMA}}), \qquad L_{\text{hist}} = \min(L_{\text{observed}}, L_{\text{EMA}})$$

With $L_{\text{total}}$ the depth of the prepared curve at its centre, only the tail is scaled:

$$\hat L_0 = L_0 \cdot \frac{\min(L_{\text{hist}}, L_{\text{total}})}{L_{\text{total}}}, \qquad \hat x = \frac{\hat L_0}{\sqrt{\hat p}},\quad \hat y = \hat L_0 \sqrt{\hat p}$$

The impact-aware value of $c$ units of collateral is what selling all of it into those reserves would return:

$$W(c) = \frac{c\,\hat y}{\hat x + c}$$

The concentrated execution curve is deliberately not used here. Concentrated depth can leave with the next recentering; the tail cannot.

Effective liquidation LTV, by position size against the conservative depth

85.0% cap77.3%56.7%42.5%0%25%50%75%100%0%25%50%75%100%

Two limits and a stored factor

A successful borrow computes and stores the position's liquidation collateral factor for that debt side, capped at 85%; if it would fall below the minimum the borrower passed in the instruction, the borrow is rejected. The liquidation limit is $W(c)$ times that factor; the borrow limit is 95% of it.

On a collateral withdrawal the program uses the greater of the stored factor and a freshly computed one, then tests the buffered capacity after the withdrawal. Full repayment clears the factor.

Each debt side is secured by the position's collateral in the opposite asset only. The public-borrow book also keeps debt-capped aggregate global-health contributions, which improve underwriting for new borrows without locking anyone else's idle collateral or changing existing terms. New borrows are also refused when they would push the market below its health floor.

The daily bucket

Each debt asset has one leaky 24-hour bucket for gross new public borrowing, sized from conservative depth: 20% by default, at most 30%. Only new public principal consumes it. Repayments and exits do not refund it, the bucket is not a trailing-window sum, and hLP funding and isolated leverage do not draw on it because they do not lend cash out, though both face their own checks and count toward utilization.

Interest

Utilization on a side counts every indexed debt once:

$$u_i = \frac{D_i^{f} + D_i^{\ell} + D_i^{h}}{D_i^{f} + D_i^{\ell} + D_i^{h} + C_i}$$

Utilization does not cap new borrowing. A loan is bounded by cash, collateral, market health and the daily bucket; when utilization runs past its band, the rate climbs instead of the loan being refused. Separately, settings bundles and concentration ramps cannot execute while either lending side is at or above 80% utilization, a fixed guard that never refuses a loan.

The rate comes from a controller that watches two things: how well first-loss capital covers the debt, and how much of the side's cash is lent out. Its coverage signal is the market's Junior LP (jrLP) capital $J$ over all the debt $D$ it covers, discounted by the side's idle cash:

$$s_i = \frac{J}{D}\,(1 - u_i)$$

Covered debt counts public loans, isolated leverage debt and hLP funding debt, valued in one quote unit, and jrLP waiting to exit still counts until it converts. Each side has two target bands: the signal band, $s_{lo}$ to $s_{hi}$ (5% to 6.25% by default), and the utilization band, $u_{lo}$ to $u_{hi}$ (75% to 80% by default). The rate rises when either is out of line and falls only when both are comfortable:

$$r(t) = \max\!\big(r_0 \cdot 2^{\,d\,t/h},\ r_{\min}\big), \qquad d = \begin{cases} +1 & s < s_{lo} \ \text{or}\ u > u_{hi} \\ -1 & s > s_{hi} \ \text{and}\ u < u_{lo} \\ 0 & \text{otherwise} \end{cases}$$

Coverage signal against utilization, at the default bands

Rate fallsRate holdsRate risesRises0%5%6.25%10%0%50%100%75%–80%

Junior capital worth 25% of the debt: the rate falls below 75% utilization, holds to 80% and rises past it.

Low utilization does not lower the rate on its own. If junior capital covers too little of the debt, the rate still rises, which draws junior capital in with higher yield or pushes borrowers to repay; either restores coverage. Ample coverage does not lower it either while cash is scarce.

Both bands are inclusive, so a side sitting on an edge holds, and with no debt there is no signal, so the rate holds as well.

While it moves, the rate doubles or halves every half-life $h$ (14 days by default). Base APR has a fixed 1% floor and no adjustable economic ceiling.

A market starts at 4% unless its creator picks another rate of at least 1%; the starting rate is creation-only and does not reset a live market. The operator or manager can change both bands and the half-life, within 12 hours to 30 days, after full notice; the edit preserves the live APR.

Borrow rate from a 4% start (log scale)

• Rising
• Holding
• Falling

Doubles every 14 daysHoldsHalves to the 1% floor1%4%16%64%0d15d30d45d60d

The program integrates the changing rate over each elapsed interval, including any time spent at the fixed floor, and accrues the borrow index with that integral. All of it happens in integer fixed point, so these continuous formulas describe the shape rather than the last digit.

Where interest goes

Interest accrues into borrowers' debt balances and is realized when they repay.

The protocol markup is charged on top of base interest. The operator receives its configured 0–50% share of base interest, and the remainder is booked to LP income ledgers.

Junior LP takes the market's junior income share (50% by default, adjustable within 10–90% after the full notice), and the rest goes to srLP, including the srLP the two hLP vaults hold. Funding interest the hLP vaults pay is split the same way, except that the vaults' own srLP takes no part. Holders collect their share when they harvest.