Interest Rate Model

The interest rate in Parallel finance is dynamically determined by the supply and demand. Therefore, the borrow and supply interests could vary in different blocks.

1. Exchange Rate

When a supplier deposits an asset to the money market, a certain amount of pTokens will be issued based on the initial exchange rate. The supplier earns interest through the appreciation of pToken's exchange rate.

$$ExchangeRate = \frac{(TotalCash + TotalBorrows - TotalReserve)}{ TotalSupply}$$

2. Utilization Ratio

The utilization rate represents the percentage of borrows in the total money market.

$$UtilizationRatio = \frac{TotalBorrows} {TotalCash + TotalBorrows}$$

3. Reserves

Parallel finance converts a certain portion of borrow interests into reserves. These reserves may be used for incentives, liquidation protection, emergencies, etc.

$$TotalReserve_{t+1} = InterestAccumulated \cdot ReserveFactor + TotalReserve_{t}$$

4. Borrow Interest Rate

Parallel Finance implements the jump interest model. When the utilization rate exceeds the kinks, the jump rate will be applied to the excess portion.

If Utilization <= Jump_Utilization,

$$Borrow Interest Rate = Base Rate + \frac{JumpRate-BaseRate}{JumpUtilization} \cdot Utilization$$

If Utilization > Jump_Utilization,

$$Borrow Interest Rate = JumpRate+ \frac{FullRate-JumpRate}{1-JumpUtilization} \cdot (Utilization - JumpUtilization)$$

5. Interest Rate Model Parameters

Asset	Base_Rate	Full_Rate	Jump_Utilization	Jump_Rate
KSM	2%	30%	80%	14.01%
xKSM	1%	26.21%	80%	10%
USDT	2%	34.21%	85%	4.67%