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Interest Rates

Dynamic Interest Rates​

Kylix uses a dynamic interest rate model that adjusts rates based on the utilization of assets within its lending pools. When the demand for loans is high, pool utilization increases, which raises the borrowing rate. This incentivizes lenders to contribute more assets, enhancing pool liquidity. Conversely, when demand is low, the interest rates decrease, encouraging borrowing and maintaining balanced liquidity levels across the platform. This dynamic balancing prevents both liquidity shortages and oversupply, optimizing the health of Kylix’s lending ecosystem.

Polynomial Interest Rate Model​

Kylix Finance employs a sophisticated polynomial interest rate model, inspired by advanced mechanisms similar to those developed for Clearpool. This model incorporates mathematical functions to create an interest rate curve that adapts based on various parameters, balancing lender and borrower incentives in line with market conditions.

The structure also incentivizes liquidity bootstrapping by providing higher interest rates at lower utilization ratios, increasing the platform's total value locked (TVL). By optimizing liquidity utilization, the model ensures competitive rates for both lenders and borrowers across supported chains, positioning Kylix as a robust solution in decentralized finance.

Cosine-Based Modulation​

A key feature of Kylix’s model is its use of a modulated cosine function to adjust interest rates dynamically. Here’s how it works:

  • Flexible rate adjustment: the cosine-based function allows Kylix to control the slope and shape of the interest rate curve, increasing rates smoothly as pool utilization grows. Rates remain low when utilization is minimal, helping Kylix attract borrowers and promote healthy pool engagement
  • Smooth scaling with utilization: by stretching the cosine function, Kylix can amplify interest rate sensitivity at higher utilization levels. For instance, the cosine function is stretched more at values approaching full utilization than at lower values. This "stretching" ensures that interest rates rise significantly when the pool is near full utilization, creating a natural deterrent against overuse and helping maintain capital availability
  • Adjustable minimums and maximums: using parameters such as the cosine function’s amplitude and frequency, Kylix can adjust the minimum and maximum interest rates for each pool. These adjustments help achieve desired outcomes without abrupt rate changes, smoothing out fluctuations in response to pool activity

Benefits of the Polynomial Model​

  • Market-responsive: the polynomial model provides a flexible response to market conditions, allowing Kylix to adjust rates dynamically based on real-time pool data
  • Capital efficiency: by optimizing rates across a range of utilization levels, Kylix maximizes capital efficiency for both lenders and borrowers, encouraging continuous liquidity inflow
  • Incentivized liquidity bootstrapping: higher interest rates at low utilization levels attract early liquidity providers, enabling faster total value locked (TVL) growth and ensuring ample liquidity for borrowers as the pool grows

Technical Formula​

The interest rate model can be expressed with the following formula:

f(x) = α ⋅ cos(2πx^n) + β [cos(2πx^n) + 1] ⋅ Θ(x − x_m) + κ

Where:

  • α and β are parameters that control the amplitude
  • n allows adjustment of the curve's minimum point, moving it right or left as needed
  • x_m is the threshold utilization point where rate changes accelerate
  • Θ(x - x_m) is the Heaviside function, adjusting the rate sensitivity near full utilization
  • κ is a vertical shift constant

This formula enables Kylix to modulate rates precisely, applying varying degrees of pressure depending on utilization levels and maintaining a stable, predictable interest rate environment for all users.