Fair APRs
Overview of how fair APRs are derived on MYSO
Since a Zero-Liquidation Loan can be seen as a swap, where the borrower pledges collateral and receives a loan amount plus an embedded call option, we need to determine a fair value for this call option first. Thus, in a fair ZLL, both the borrower and lender should not be better or worse off at inception of this swap.
Let’s visualize a theoretical loan to understand how to fairly price a ZLL:
Assume a borrower has arrived on MYSO v2 and wants to take on a loan and borrow $1500 worth of USDC against their ETH collateral worth $2000 for 90 days (75% LTV).
To make the swap fair, the borrower should receive a call option which is worth $500 because this way the position value pre- and post- borrow is the same. In this situation, how should a lender choose the strike price of the embedded call option such that its fair value is $500, and how will the prospective yield be determined?
The most common way to price a call option is to use the Black-Scholes model, which takes into account several factors, including the current price of the collateral, the risk-free rate, price volatility of the collateral, the loan tenor, and the strike price. Other models and pricing methodologies exist, so it’s up to market participants to decide how they want to go about pricing these embedded options to come to a fair loan valuation. Under Black-Scholes assumptions, for this loan:
1 ETH is worth $2000
You buy a European call option with a loan tenor of 90 days, where ETH volatility is at ~80% and the theoretical risk-free rate is 4%.
For the value of the call option to come out to be $500, the strike price would have to be ~$1661.
In this scenario, if 1 ETH worth $2000 is swapped to receive a loan of $1500, as well as this call option worth $500, the strike for this option would be ~$1661 and we would have a situation where the position is fairly priced with no party better or worse off.
Let’s consider the above example and translate it into an APR — if a borrower takes the $1500 loan and ends up repaying the $1661 strike price to reclaim their collateral prior to expiry (90 days), the implied APR would be 42.9% — this means that the term rate, or rate adjust for the loan period, would be around ~10.73%.
Visualizing Fair APR differences
We can visualize how different loan tenor/LTV combinations affect fair strike prices and implied APRs for this same loan in which a borrower puts up 1 ETH (= $2000) with ETH at an 80% implied volatility.
You can see how Black-Scholes-derived fair APRs do increase for higher tenor/LTV combinations, which intuitively makes sense as lenders bear more duration risk and hence expect to receive a higher APR to be compensated for this.
Implied volatility also has a profound effect on the fair pricing of a ZLL —if we increase the volatility of ETH to 100% rather than 80%, we can see higher APRs for the same tenor/LTV combinations as well more pronounced variations across the same combinations.
It is important to consider that although the Black-Sholes pricing model is a common tool for fair-strike option pricing, the underlying option logic on MYSO is akin to American option expiries rather than European options, meaning that the option can be exercised (underlying collateral can be reclaimed) at any time prior to expiry rather than only at the expiration date. Since the underlying smart contracts are oblivious towards the pricing of these options, market participants are able to benefit from loan fair-value mispricing and non-linear risk transferal through the use of Black-Scholes or other option pricing models. This means that there will also be opportunities for both counterparties to capture fair-value arbitrations on mispriced loans.
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