Variable Interest Rate
Supply side incentive - reduce the supply
When we find that there is too much xUSD in the market and the price has fallen to below $1.00 the primary method we have to convey this information to the market is to increase the vault interest rate. An increasing interest rate signals to vault holders that they should purchase xUSD and pay off their debt due to increasing borrowing costs. The purchasing of xUSD for repayment will pull the token off of the market, re-balancing in the direction of xUSD = $1.00. The equation that governs this dynamic interest rate is recorded below.
Where:
I is the interest rate
p is the price of xUSD
B is the base interest rate (3%)
Using this formula to set the borrowing rate for xUSD results in a curve that increases with distance from the $1.00 peg as seen below.
Below are the steady state borrow rates for different xUSD prices as derived from the interest rate equation.
$1
3.00%
$0.99
5.62%
$0.98
8.34%
$0.97
11.15%
$0.96
14.06%
$0.95
17.09%
$0.94
20.23%
$0.93
23.49%
$0.92
26.87%
$0.91
30.39%
$0.9
34.04%
$0.89
37.84%
$0.88
40.00%
$0.87
40.00%
Since the safety of vault holders is a high priority, there are two of safety precautions that have been instituted to make sure that interest rates don't go so high, so fast that vault holders are liquidated with no time to adjust their strategy.
The first safety precaution is a limitation on the interest rate growth rate. In any 24 hour period, the interest rate can only change a maximum of 4%. This means, that if someone leverages their vault position heavily and pushes the ecosystem off peg down to $0.97, it will take three 24 hour periods for the full interest rate of 11.15% to be reached.
The second precaution is that an interest rate cap of 40% applies to the curve after around $0.88. Despite this plateau in interest rate, 40% APR is a strong incentive to take advantage of the cheap xUSD and pay down vault debt.
The actual application of the variable interest rate is accomplished by a script that checks the price of xUSD every 14 hours. At that point, necessary adjustments are made to the borrow rate and the system continues on with the new rate.
The price and borrow rate of xUSD can be viewed on the CompX analytics page. This page updates its content every 15 minutes.
Because this only affects vault holders, only a relatively small portion of xUSD users are incentivized by this method alone. To put the power of peg control in more hands, a second stability mechanism has been implemented. xUSD staking is a control mechanism that is accessible to many more users. Anyone that's opted into the token can be involved.
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