> For the complete documentation index, see [llms.txt](https://docs.3jane.xyz/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.3jane.xyz/levered-callable-capital-lcc/mechanism/defaults.md). # Defaults A called staker either funds their obligation or lets the auction replace them, and each path has a computable cost. Figures below use the worked example's terms; the hurdle rate is illustrative. ### The cost of funding Funding an obligation `x` costs whatever it costs to have `x` liquid inside the funding window: ``` cost of funding = c * x ``` where `c` is the staker's cost of making `x` liquid for the window: near zero for capital already sitting in stables, and slippage plus forgone yield for positions that need unwinding. Stakers are underwritten to be heavily overcapitalized against their promise, so funding is normally an unwind rather than a borrow. Even the outlier case is cheap: borrowing the full amount at a 10% annual rate for the 9-day window costs `10% * 9/365 = 0.25%` of `x`, roughly $123 on a $50,000 obligation. ### The cost of defaulting Default slashes the full margin into the auction pool, and the auction returns everything except what it takes to attract a fill: ``` cost of default = award(s*) + fee ``` where `award(s*)` is the margin the auction clears at. The clearing is bounded below by the marginal bidder's hurdle `h` on the missed amount, plus one step of granularity: ``` award(s*) >= h * x ``` At launch terms with the worked example's 10% hurdle, a $50,000 miss against a $75,000 bond clears at step 9 of the auction, about 4.5 hours into the window, for a $5,483 award: defaulting cost $5,483, or 11% of the missed amount, against roughly $123 to fund it. ### When defaulting is economical Comparing the two costs: ``` default is economical only when c * x > h * x + fee ``` which reduces to `c > h`. The hurdle `h` prices a third party's capital, their risk, and the 35-day cooldown they accept, so it sits far above the 9-day cost of liquidity available to any solvent, overcapitalized staker. The inequality flips only when `c` is effectively unbounded: the staker cannot raise `x` at any price inside the window. True illiquidity is the only economical default, which is exactly the event the backstop exists to absorb. The penalty is not a chosen parameter but the market price of replacement liquidity at that moment: cheap when bidders are abundant, expensive when they are scarce. ### When the auction clears A bidder fills as soon as the rising offer clears their hurdle: ``` offered(s) = A_max * (1 - (1 - d)^s) fill at the first s where offered(s) >= h * shortfall ``` The offer ramps every step, so a shortfall fills at the first step that clears the hurdle of any bidder present, and competition pulls the clearing toward the lowest hurdle in the room. If no bidder participates, the window ends unfilled and the pool is forfeited; the mechanism prices rational behavior, it does not conjure it. The award is margin the bidder receives instantly against USDC they would deploy into USD3 anyway, so `h` floors near the bidders' opportunity cost over USD3 rather than at distressed-liquidity levels. ### Counterparty risk from leverage The margin is a bond, not the funding source: at a 7.5% margin ratio the deliverable is 13.33x what the facility holds, so delivery depends on the staker's balance sheet outside the facility. That is the counterparty risk the leverage introduces, and it is modelled at admission. Each address is underwritten for overcapitalization against its promise: ``` coverage = verified capital / promise ``` `p_default` falls as coverage rises, because a covered staker funds by unwinding rather than by raising. The margin prices a failure, the underwriting bounds how often one happens, and the backstop absorbs what remains, so certainty of execution is layered: a call is funded by stakers with probability `1 - p_default`, by bidders against the slashed margin otherwise, with any unfilled residual carried forward by 3Jane. ### Correlated stress The inequalities above hold per staker; the systemic question is whether many stakers hit `c > h` at once, in the same state of the world where bidder hurdles spike. Three design choices work against that correlation: * Calls open on deployment demand at 3Jane's chosen timing, a deal ready to fund, not on market distress. A bank revolver is drawn hardest in a crisis; an LCC call opens when there are assets ready to fund. * The 9-day funding window prices orderly unwinds rather than fire sales, so a staker's `c` reflects calm-market liquidity. * Stakers are underwritten for overcapitalization and self-select for wanting USD3 exposure, so funding a call moves capital where the staker already intended it. Correlation is bounded, not eliminated: a broad liquidity crunch raises every `c` and every `h` together, and in that state the unfilled branch above applies. The design reduces exposure to it by choosing when calls open; it does not remove it. ### Expected defaults With funding dominant for every solvent staker, the modelled default rate on a call is the insolvency rate of an underwritten cohort rather than a strategic choice: ``` expected shortfall = p_default * call size ``` Underwriting each address at staking keeps `p_default` low, and the expected shortfall, not the gross call, is what the backstop has to clear; see [Backstop sizing](/levered-callable-capital-lcc/mechanism/backstop-bidders.md#backstop-sizing).