Abstract: Compare the advantages and disadvantages of the interest rate model.

There are a variety of DeFi loan services based on pools on the market, each offering a different interest rate model to maintain a balance between lenders and borrowers' needs.

The interest earned by the depositor from the DeFi loan service based on the pool is directly proportional to the interest created by the borrower. Therefore, it is most desirable for depositors to lend as much token service as possible at the highest possible rate. At the same time, from the perspective of the borrower, it is beneficial to borrow at the lowest possible interest rate, so it is crucial to find a balance between the two parties.

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The main factor in this process is utilization. For these fund-based DeFi loan services, the pool of funds is maintained by the funds deposited by the lender, and the lender withdraws the loan from the pool of funds. Utilization is an indicator of the lending of funds (total borrowings), and the total loanable amount of the token (total deposit + agreement interest) is another indicator.

In general, high usage rates indicate a higher percentage of the pool of funds used for loans, so depositors have higher interest rates. Conversely, lower utilization means less loans and lower interest rates.

**This mechanism for determining interest rates has two main purposes:**

**1. High deposit interest rate**

It is imperative to provide high interest rates for deposits and increase the utilization rate of deposits.

If the needs of lenders and borrowers are met at current market rates, higher utilization rates will result in higher interest rates for depositors. This creates a healthy intensive loop in the system. However, if interest rates are low, interest rates offered to depositors will be low, reducing their incentive to keep funds in the system. This will lead to an increase in withdrawals, resulting in a continuous reduction in the pool of funds. This ultimately leads to a reduction in the activity of the system.

**2, stable withdrawals**

In order to be able to respond to withdrawal requests in a unified manner, it is important to maintain a certain amount of funds available for immediate withdrawals. If the system is unable to process all withdrawal requests, the possibility of a bank run is increased. This will undermine the reputation of the system and lead to user churn. In order to prevent this from happening, the utilization rate must be kept at a certain level. If the interest rate is close to 100%, it is necessary to encourage the withdrawal of borrowed funds or increase deposits by rapidly raising interest rates to ensure the liquidity of the pool.

As you can see, the interest rate model plays a crucial role in the DeFi loan service based on the pool of funds. Each service takes a lot of time and effort to perfect the model.

The following is an in-depth analysis of various DeFi loan services and their interest models. The DeFi projects selected for this article include: compound, Fulcrum, dYdX, DDEX, and Divine. Their interest rate models fall into three main categories: **linear models, polynomial models, and exponential models.**

**Linear model**

Compound and Fulcrum use a linear interest rate model.

*Linear interest rate model (Compound and Fulcrum)*

As utilization rates rose from 0% to 100%, Compound's interest rate remained at [5%, 20%] and Fulcrum's interest rate remained at [8%, 100%].

1. At the current market interest rate (DAI is 12.5%), Compound achieves a balance of 50% utilization, while Fulcrum is at 61.3%, Compound <Fulcrum.

2. At 90% utilization, the Compound slope is 0.15, the Fulcrum slope is 8.2125 (the derivative at x = 0.9+), and Compound<Fulcrum,

We assume that the configuration of the withdrawal pool is 10%, so we chose 90% utilization for comparison.

For simple linear models such as Compound, you must choose a lower slope to get a higher utilization. When the utilization rate is higher, the utilization rate is lower to achieve a stable pressure compared with other models, and the model has a large bank run risk. However, Fulcrum introduces another linear model with a certain value, which reduces the risk of the model.

**Polynomial model**

dYdX and DDEX are services that use polynomial models to calculate interest rates.

*Interest rate polynomial model (dYdX, DDEX)*

As the utilization rate increases from 0% to 100%, the interest rate of dYdX remains at [0%, 50%], and the interest rate of DDEX remains between [10%, 100%].

1. Under the current market interest rate, dYdX achieves a balanced utilization rate of 75.5% and DDEX of 49.1%. (dYdX< DDEX)

2. At 90% utilization, the dYdX slope is 1.55 and the DDEX slope is 3.08 (the derivative at x = 0.9+) (dYdX < DDEX)

The interest rate of the polynomial model rises sharply as the utilization rate approaches 100%. Compared with the linear model, the polynomial model can better realize the stability of funds and facilitate the withdrawal of funds.

**Index model**

Finally, Divine is a service that uses the interest rate index model. (currently used by Trinito)

*Interest Rate Index Model (Divine)*

As the utilization rate rose from 0% to 100%, Divine's interest rate remained at [3%, 100%]. The minimum interest rate is set by the value b and the slope is determined by the value a.

1. At the current market interest rate, Divine achieved a balanced utilization rate of 88.4%.

2. At 90% utilization, Divine's slope is 2.63. (x = 0.9+ derivative)

The exponential model is similar to the polynomial model, which can increase interest rates rapidly when the utilization rate is high, and increase the motivation for capital to achieve liquidity. Similarly, as can be seen from the above figure, a high coefficient of curvature (a = 20), below a certain utilization rate (70%), can provide a fairly constant interest rate. This is a big advantage because the system provides liquidity and interest rate stability without additional intervention, essentially addressing the risks inherent in most pool-based DeFi loan services.

As you can see, each DeFi loan service has a different interest rate model that suits its service. Therefore, it is difficult to say which one is perfect. These are all undergoing market testing, and the work of improving the interest model mechanism and improving efficiency will continue.

*Author: Divine Protocol*

*Compile: Sharing Finance Neo*