Liquidity and Interest Rates on ERC-20 Fungible Tokens

Introduction

The liquidity of the the Parallel protocol represents the availability of capital to support borrowing amounts and redeeming nTokens and pTokens. The liquidity of the protocol can be measured via the utilization rate, which is the share of reserve that is currently borrowed for each asset.

Interest Rate Model

Interest rates are charged to borrowers based on the Utilization Rate, $U$. At a high level, the interest model helps incentivize what is needed to support liquidity. When there is capital available, borrowers pay less interest to borrow; when capital is scarce, high interest rates encourage more supply and repayments on loans.

As $U$ gets closer to 100% the liquidity risk increases. There is an inflection point before which the interest rate changes, i.e. slope or $\frac{dR}{dU}$, are small and after which slope starts rising sharply. This inflection point is represented as $U_{optimal}$.

The interest rate$R_t$follows the model:

$if \hspace{1mm} U < U_{optimal}: \hspace{1cm} R_t = R_0 + \frac{U_t}{U_{optimal}} R_{slope1}$

$if \hspace{1mm} U \geq U_{optimal}: \hspace{1cm} R_t = R_0 + R_{slope1} + \frac{U_t-U_{optimal}}{1-U_{optimal}}R_{slope2}$

In the borrow rate technical implementation, the calculateCompoundedInterest method relies on an approximation that mostly affects high interest rates. The resulting actual borrow rate can is:

$Actual APY = (1+Theoretical APY/secsperyear)^{secsperyear}-1$

Model Parameters

Asset	UOptimal	r_0	Slope 1	Slope 2	Reserve Ratio
ETH	85%	5%	8%	60%	10%
stETH	85%	0%	8%	60%	10%
wstETH	85%	0%	8%	60%	10%
USDC	85%	5%	8%	60%	10%
USDT	85%	5%	8%	60%	10%
APE	85%	40%	25%	50%	10%
sAPE	85%	40%	25%	50%	10%
cAPE	85%	5%	10%	23%	10%
BLUR	85%	0%	8%	60%	10%