A variety of pool-based DeFi lending services currently exist in the market at the moment and each of these services offer different interest models that maintain equilibrium between the needs of lenders and borrowers.

The interest depositors receive in pool-based DeFi lending services is directly proportional to the interest created from borrowers. Therefore, for depositors, a service that lends as many tokens as possible, at an interest rate as high as possible, is the most desirable. Meanwhile, from a borrower’s standpoint, it is beneficial to borrow at the lowest rate possible thus finding the balance between these two aforementioned parties is crucial.

The main element during this process is utilization rate. For these pool-based DeFi lending services, the pool is maintained by the funds deposited by lenders and borrowers take out loans from this pool. Utilization rate is an indicator of how much funds have been loaned out (Total borrows), compared with the total lendable amount of tokens (Total deposits + protocol equity). Usually, a high utilization rate indicate a higher percentage of pool used for lending; thus, a higher interest rate for depositors. Inversely, a lower utilization rate means less loans made, and lower interest rate.

This mechanism for determining interest rate serves two major purposes.

1) High deposit interest rate

To provide a high interest rate for deposits, it is imperative to raise utilization rate. Provided that the demands of lenders and borrowers are met at the current market interest rate, a higher utilization rate will yield a higher interest rate for depositors. This creates a healthy reinforcement cycle within the system. However, if the utilization rate is low, the interest rate provided to depositors will be low as well, leaving them less incentives to keep the funds in the system. This will result in an increase in withdrawal, causing the pool to decrease continually. This ultimately results in lowered activity for the system.

2) A stable withdrawal response

To be able to respond to withdrawal requests uniformly, it is important to keep a certain amount of funds available for immediate withdrawal. If a system is unable to process all withdrawals upon request, possibility of a bank run is increased. This will undermine the credibility of the system, and result in a loss of usership. To prevent all of this from happening, the utilization rate must be kept under a certain level. Should it approach 100%, recuperation of funds loaned out or additional deposits must be encouraged through a rapid rise in interest rate, securing the liquidity of the pool.

As you can see, interest rate models serve a vital function in pool-based DeFi lending services. Needless to say, each of these services spend a large amount of time and effort perfecting the models. The following is an in-depth analysis of various DeFi lending services and their interest model for DAI lending. The services chosen for this analysis are Compound, Fulcrum, dYdX, DDEX and Divine, and their interest models fall largely under three categories — linear, polynomial and exponential. (As of 23 Sep, 2019)

(1) Linear Models

Compound and Fulcrum are services that use the linear model for interest rate.

Linear model for Interest rate ( Compound, Fulcrum )

As utilization rate rises from 0% to 100%, interest rates stay between [5%, 20%] for Compound, and [8%, 100%] for Fulcrum.

1) With the current market interest rate of DAI (12.5%), Compound achieves equilibrium at 50% utilization rate and Fulcrum at 61.3%. (Compound < Fulcrum)

2) At 90% utilization rate, Compound shows a slope of 0.15, Fulcrum shows 8.2125 (Derivative compared at x = 0.9+) (Compound < Fulcrum)

We are assuming 10% allocation of the pool for withdrawal, and thus have selected 90% utilization rate for comparison.

For simple linear models like Compound, a lower slope must be chosen to achieve high utilization rate. When the utilization rate is high, the pressure to lower utilization rate, to achieve stability, is lower compared to other models, and the risk of bank run is quite possible in this model. However, Fulcrum introduces another linear model at a certain value, mitigating the risk that this model possesses.

(2) Polynomial Models

dYdX and DDEX are services that use the polynomial model for interest rate.

Polynomial model for Interest rate ( dYdX, DDEX )

As utilization rate rises from 0% to 100%, interest rates stay between [0%, 50%] for dYdX, and [10%, 100%] for DDEX.

1) With the current market interest rate of DAI (12.5%), dYdX achieves equilibrium at 75.5% utilization rate and DDEX at 49.1%. (dYdX < DDEX)

2) At 90% utilization rate, dYdX shows a slope of 1.55, DDEX shows 3.08 (Derivative compared at x = 0.9+) (dYdX < DDEX)

Polynomial models’ interest rates rise sharply as utilization rate approaches 100%. Compared with linear models, polynomial models are better at achieving stability of funds, for withdrawal purposes.

(3) Exponential Models

Lastly, Divine is a service that uses an exponential model for interest rate. (Currently used by Trinito)

Exponential model for Interest rate ( Divine )

As utilization rate rises from 0% to 100%, interest rates stay between [3%, 100%] for Divine. Minimum interest rate is set through value b, and the slope rate determined by value a.

1) With the current market interest rate of DAI (12.5%), Divine achieves equilibrium at 88.4%.

2) At 90% utilization rate, Divine shows a slope of 2.63. (Derivative value at x = 0.9+)

Exponential model, much like polynomial model, can rapidly increase the interest rate when utilization rate becomes high, increasing the momentum towards achieving liquidity of funds. Also, as seen through the graph depicted above, with a high curvature coefficient(a = 20), a fairly fixed interest rate can be provided at utilization rate below a certain level (70%). This is a big advantage, as this system can provide stability in liquidity and interest rate without extraneous intervention, essentially solving the risk inherent to most pool-based DeFi lending services.