> For the complete documentation index, see [llms.txt](https://nysa-finance.gitbook.io/nysa/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://nysa-finance.gitbook.io/nysa/architecture/interest-rate-model.md).

# Interest Rate Model

### Strategy Overview

Nysa Finance manages liquidity through a dynamic interest rate model. We adopted the Aave V3 Kinked Rate mechanism because it is a proven industry standard for balancing capital efficiency with pool security.

The system automatically adjusts rates based on the Utilization Rate ($$U$$), ensuring sufficient liquidity is always available for withdrawals. The Utilization Rate is calculated as follows:

$$
U = \frac{\text{Total Borrows}}{\text{Total Liquidity}}
$$

### How it works

The interest rate follows a two-segment curve (the "kink") anchored around an Optimal Utilization point ($$U\_{optimal}$$).

#### 1. The Formulas

* When $$U \leq U\_{optimal}$$: Rates stay low to keep borrowing affordable.

$$
R\_t = R\_0 + \left( \frac{U}{U\_{optimal}} \right) \times \text{Slope}\_1
$$

* When $$U > U\_{optimal}$$ — Rates increase sharply to prevent pool exhaustion, incentivizing borrowers to repay and lenders to deposit:

$$
R\_t = R\_0 + \text{Slope}*1 + \left( \frac{U - U*{optimal}}{1 - U\_{optimal}} \right) \times \text{Slope}\_2
$$

#### 2. Supply Rate

Lenders earn a proportional share of the interest paid by borrowers, net of a *Reserve Factor* retained by the Nysa treasury:

$$
\text{Supply Rate} = R\_t \times U \times (1 - \text{Reserve Factor})
$$

### Key Metrics

* $$R\_0$$: The base interest rate (floor rate).
* *Slope 1*: The rate of interest growth below the optimal utilization threshold.
* *Slope 2*: The aggressive rate of interest growth above the optimal utilization threshold (protection mode).
* *Reserve Factor*: A protocol fee retained in the Nysa treasury for risk management and protocol sustainability.

***