Fair APRs

Overview of how a fair APR is derived on MYSO v1

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 LP should not be better or worse off immediately after a ZLL swap has been made.

The most simple 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 also exist, so it’s up to market participants to decide how they want to go about pricing these embedded options and come to their own fair valuation.

Under Black-Scholes assumptions, let’s assume that 1 ETH is worth $1500 and you want to buy a European call option with a loan tenor of 30 days, where ETH volatility is at ~100% and the risk-free rate is 2%. For the value of the call option to come out to be $800, the strike price would have to be $702.

So, if we were to swap 1 ETH worth $1500 to receive a loan of $700, as well as this call option worth $800, we would have a situation where the position is fairly priced, as we are not better or worse off.

Let’s consider an example and translate it into an APR — if a borrower takes out this $700 loan and ends up repaying a $702 strike price to reclaim their collateral prior to expiry (30 days), the implied APR would be 3.4%.

APR function where L= loan amount, K = strike price, and T = tenor

Let’s take a look at how several loan tenors and LTVs affect fair strike prices and implied APRs given that a borrower puts up 1 ETH (= $1500) with 100% implied volatility.

The Black-Scholes-derived fair APRs do increase for higher LTVs and longer tenors, which intuitively also makes sense, as LPs bear more risk and hence expect to receive a higher APR to be compensated for this.

It also becomes evident that as you increase volatility levels (from 100% to 150%), higher APRs are generated and there are more pronounced differences between the individual LTV-vs-tenor APR combinations.

It is important to consider that although the Black-Sholes pricing model is a nifty tool for fair-strike option pricing, MYSO uses American option expiries rather than those of 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.