# Announcing Fringe’s improved interest rate model

# Snapshot of Our Current Situation

Until recently, Fringe’s permissionless Leveraged Trading and Lending Platform (PLP) had used Compound’s interest rate model, which we saw could be optimized to significantly improve capital efficiency — by targeting a higher borrower utilization rate of Fringe’s capital markets. Fringe’s improved interest rate model is now currently operating in all Fringe’s current mainnet production instances.

# Understanding Utilization Rate

The utilization rate represents the percentage of lender funds that are currently being borrowed. For example, if lenders have deposited $100 and $20 has been loaned out, the utilization rate is 20%.

## Importance of Utilization Rate

The utilization rate is crucial because it indicates how efficiently lender funds are being used. A low utilization rate means that a large portion of lender funds is idle and not earning any yield. Our goal with Fringe’s new interest rate model is to maximize the utilization of lender funds, thereby increasing lender revenue and decreasing costs for borrowers.

We do not aim for a 100% utilization rate, as this would prevent lenders from withdrawing their funds. Instead, we target a utilization rate of 70%, balancing the need for sufficient liquidity for withdrawals with maximizing the yield on lenders’ capital. (This target utilization rate is a configurable governance parameter and may change over time or for individual capital markets.) This new model increases profitability for lenders.

## Changes

The old model, which is used by most other lending platforms, is a simplistic model that uses a fixed mapping between the utilization rate and the interest rate. For instance, the interest rate might be set to 6% when the utilization rate is 60% and 6.5% when the utilization rate is 70%.

Our new model targets a specific utilization rate by dynamically adjusting the interest rate to encourage lending and borrowing as needed. The interest rate decreases when the utilization rate is below the target, incentivizing borrowing. Conversely, the interest rate increases when the utilization rate exceeds the target, encouraging more capital deposits. These adjustments aim to maintain a utilization rate around the target utilization rate.

The new interest rate model significantly increases the profitability of lending on Fringe, at the expense of slightly lower liquidity arising from a target util rate < 100%.

# Diagrammatic Representation of Interest Rate Changes and Utilization Rates

The diagram below shows how interest rate changes (per week) relate to the capital pool utilization rate (in %).

Note the y-axis plots the *rate of change* of the interest rate, not the interest rate itself.

The interest rate change ranges between -5% and 5% per week. When the utilization rate is below target utilization rate, interest rate changes are negative, increasing linearly and proportionally up to the target utilization rate. Beyond the target utilization rate, the interest rate change per week increases linearly at a higher rate, reaching a change of 5% when the utilization rate is 100%.

## Detailed Mathematical Explanation

The variables used in the new model are:

**InterestRate**: The current interest rate.**CurrentUtilizationRate**: The percentage of total lender funds currently borrowed.**TargetUtilizationRate**: The desired percentage of lender funds to be borrowed.**GainFactor**: A factor used to determine the adjustment rate of the interest rate.**JumpGain**: An additional factor applied when the current utilization rate exceeds the target.**AnnualBorrowerInterestRate**: The annualized interest rate used for calculating accruals.**PreviousInterestRate**: The value of the annual borrower interest rate calculated the last time the calculation was run.**TimeElapsed**: The number of years since the last calculation.**InterestRateChange**: The annual change in the borrower interest rate.**Error**: The difference between the current utilization rate and the target utilization rate, expressed in percentage points.

When running the model:

- If the CurrentUtilizationRate is less than the TargetUtilizationRate:

InterestRateChange = Error × GainFactor

- Otherwise (if the CurrentUtilizationRate is greater than the TargetUtilizationRate):

InterestRateChange = Error × GainFactor × JumpGain

The interest rate is then calculated as:

AnnualBorrowerInterestRate = PreviousInterestRate + (TimeElapsed × InterestRateChange)

# Conclusion

We believe this improvement is a key part of the Fringe’s mission and sets us apart from the competition. As we continue to roll out new features, optimizing them will be crucial. These features include multi-chain support, atomic loan repayments, additional lender assets, dozens of collateral tokens, and support for liquidity provider tokens as collateral.

## About Fringe Finance

Fringe Finance is a decentralized money market designed to unlock the capital spread in crypto assets regardless of their capitalization and supported network. With a next-generation DeFi lending & borrowing ecosystem, Fringe aims to unlock the dormant capital from traditional financial markets and all-tier cryptocurrencies.

For more information on Fringe Finance, visit our website.