A couple of points of clarification:
The way it works is that if ZUSD value goes above $1.10, then anyone can borrow ZUSD at 110% collateral ratio, forfeit the collateral, and sell the ZUSD for more than $1.10 to make a profit. This arbitrage will cap the value of ZUSD at 110%.
You have to take the origination fee into account here, too. Re-doing your math:
Assumptions
Origination fee = 0.5%
Minimum collateral ratio = 110%
For there to be an arb gap, the (max borrow amount * ZUSD price) must be > 1.10. We can calculate max borrow amount for each 1.10 USD worth of collateral at an origination fee rate of 0.5% using this formula, which gives us a max borrow amount of 0.99502.. ZUSD. So the arb opp exists when the ZUSD price is ≥1.1055 (math).
Applying the same logic here:
But what if it costs 12% to take out a ZUSD loan? The required collateral is 110% of total ZUSD debt. But total ZUSD debt = 112% of issued ZUSD, and the arbitrageur only gets to sell the issued ZUSD. So cost of the loan = 1.10 (total ZUSD) = 1.10 (1.12 issued ZUSD) = 1.232 issued ZUSD. That means the collateral cost is 123.2% to defend the peg ceiling.
Your final result is correct. Breaking it down using my same formulas above:
Assumptions
Origination fee = 12%
Minimum collateral ratio = 110%
Again, for there to be an arb gap, the (max borrow amount * ZUSD price) must be > 1.10. We can calculate max borrow amount for each 1.10 USD worth of collateral at an origination fee rate of 12% using this formula, which gives us a max borrow amount of 0.89285.. ZUSD. So the arb gap exists when the ZUSD price is ≥1.232 (math). Let’s call this the “ZUSD arb price”.
Now we have a so-called stablecoin that is pegged between $1 and $1.232. That loose peg directly reduces the usefulness and therefore the demand for ZUSD.
I expect that most users will not interface with ZUSD directly, and those that do (e.g. stability pool depositors) aren’t directly affected by the fiat exchange rate (if anything, they’re happy to sell their ZUSD for more BTC than they would normally receive if liquidations occurred at the same price level). Most users will interface with DLLR, of which ZUSD is only one component. If the price of DLLR goes up higher than the ZUSD arb price, then there’s an incentive to borrow ZUSD and arb the price down to the ZUSD arb price. After that, there is still another option to continue arbing down to the peg target of 1 USD: use Money On Chain to convert BTC into DOC, use Mynt to convert DOC into DLLR, then sell the DLLR into the market at a profit, rinse and repeat until the arb gap is closed.
Money On Chain cannot absorb an infinite amount of BTC so this has its limits. For example currently the max amount of DOC that can be minted is around 8.3 million DOC.
This figure can be found under “DOC - Available to mint” here.)
But it is important to know that this is an option if the DLLR peg breaks upward.