Risk model

Synthetic assets and decentralized stablecoins will continue to be stable in value if borrowers either have excess collateral or if the insurance pool is sufficiently capitalized. Equilibrium stress tests collateral and bailsman pools on-chain, and the incentivizes borrowers or bailsmen  by scaling the interest rate, depending on the available liquidity. 
Equilibrium uses a methodology similar to the SEC’s Theoretical Intermarket Margining System (TIMS). The idea is that margin should be set to the maximum loss the portfolio would incur under adverse market scenarios. 
Equilibrium calculates system losses in the following way:
Calculate value of the collateral/bailsman/debt pool in normal market conditions.
Calculate collateral/bailsman/debt pool risk (portfolio volatility). 
Calculate discounts (Value at Risk) for each pool given confidence value and pool volatility.  
Calculate the value of the collateral/bailsman/debt pool in stressed market conditions.
Calculate insufficient collateral:  insufficient_collateral = max[0, debt_value * (1 + debt_discount) - collateral_value *(1 - collateral_discount)]
Compare insufficient collateral with stressed insurance value to calculate the scale: 
scale = (insufficient_collateral / stressed bailsman pool value)^alpha 
Scale is initially bounded between 0.5 and 2. Alpha is a parameter that drives the steepness of the scale curve. 
If there is more insufficient collateral than there is stressed bailsman liquidity, the scale is > 1 and the borrowers' interest rates scale higher. If there is excess bailsman liquidity, the scale is < 1 and borrower interest rates scale lower. This market mechanic strives to achieve equilibrium in system solvency. 
Insufficient collateral, however, can be a deceptive measure. Consider the following hypothetical system configuration:
User
Collateral
Debt
LTV
Borrower1
$ 500,000
$1
5000000%
Borrower2
$ 500,000
$400,000
125%
It makes no sense to include Borrower1's collateral and debt into aggregate values when calculating system risk, as this position is virtually risk-free and would lead to improper calculation of insufficient collateral. Equilibrium sets a cap on portfolio LTV, beyond which the portfolio is considered to be riskless.

So far we've covered risks related to expected and unexpected losses, but we haven't touched on the risks related to excess losses going beyond the stress levels we've set (the right tail in the chart above). In other words, what do we do when the bailsmen themselves get liquidated? Equilibrium uses treasury pool as a third line of defense, where EQ funds that accumulate from interest fees in the treasury are used to cover bailsmen losses.      

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Interest rates model

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