Solvency Providers (SPs) are thus effectively writing a bundle of puts, pooling Debtors' idiosyncratic credit default risks such that the total risk of the bundle is less than the risk of any component therein. Pooling as such brings together pricing and risk, socialising gains and losses among all participants. It’s best to segue into this topic by way of walking through an abstract scenario.
Suppose that system risk is currently on target (explained shortly), and a Debtor well below maximum LTV accrues more debt, consequently agreeing to pay extra in protection premiums (PP). This incremental borrowing cost is a reaction to the protocol’s realtime stress test reporting that, all else being equal, system solvency would be rendered slightly worse from bearing the incremental debt, representing an increase to the expected loss (shortfall) in the worst 10% of cases (extreme stress) over the course of an average year. Solvency represents how healthy the protocol’s exposure is to this risk. To be insolvent means current financial backing is insufficient in regards to a moving Capital Requirement (CR) needed to survive a shortfall in system collateralisation from extreme market stress.
Solvency Ratio (SR) compares the amount of capital backing the system at any given time relative to the CR. In an effort to bring the ratio back on target, pricing will be scaled slightly higher for every Debtor in order to induce less borrowing and attract more deposits (increase in borrowing cost translates directly to a higher yield for SPs). Changes to system state are accounted for as a credit or debit against the system risk budget, as Debtors repay debts, add collateral, or collateral prices drift. Budgeting as such considers a best estimate for the value of the protocol’s liabilities in normal market conditions, and a stress model for what their shocked value might be within a range of certainty. The model suggests the shape of a volatility smile that constantly shifts and twists up and down according to a scale factor, which changes the shape of the curve to adjust PP pricing for every Pledge.
The protocol constantly simulates a portfolio loss distribution with three categories of loss resulting from normal, above normal, and excessive market stress. Three key inputs to this model are: the correlation between the prices of each collateral type in the system, their probabilities of having an extreme price event, and the resulting dollar loss realised. SPs must vote their opinion of the implied volatility (a metric that captures the market's estimated view of the likelihood of future moves in a collateral’s supply and demand), moving the median Target SR, a live median weighed by the depositor’s % contribution to solvency and the time since their last vote. If SPs wish to actively avoid having to choose a numerical target, they may exercise a more qualitative choice by delegating their voting weight to quiDAO members.
It is worth noting that the risk budget interprets every Debtor as also being a contributor to solvency, though naturally less so than SPs having no debt. SPs only become liable in stressed markets when they absorb debt, thereby also becoming Debtors. "Own Funds” is the value escrowed by SPs, above the market value of funds at risk (Debtor’s collateral). How much Own Funds is sufficient to service all debt in the event of market stress, thus ensuring that QD is fully backed? It’s the change in Own Funds between normal and stressed markets, with SR as the ratio of Own Funds / CR.
The stress model is used primarily to simulate unexpected loss to obtain CR, SR, and the Risk Adjusted Return on Capital. RAROC states how much insurers are earning, adjusted for how much risk capital they are staking. It is a ratio describing how much net profit is being earned over and above the absorption of defaulted debt: (Revenues - Expected Losses) / CR. Knowing RAROC, SPs can assess their portfolio’s performance against how efficiently the protocol is using the risk budget (measured in earnings per unit of CR), and optimise their collateral mix. SPs escrowing more collateral that's more diverse earn most.