# π§Pools

Passif Management

Users can deposit their assets into Morphine pools to provide liquidity for borrowers. By doing so, they can earn yields on their deposited assets. Pools are tokenized and respect the ERC4626 standard so you could use it elsewhere in the DeFi space.

Differents borrow module can be plugged :

(Under) Collateralized loan Module (available)

Flash Loan Module (building)

Unused capital allocator ( maybe in the future )

The interest rate can be changed at any time:

Linear IRM (available)

PID IRM ( building )

Morphine pools accept a wide range of collateral types, including LP, LSD and ERC4626. This flexibility offer great opportunities for borrowers but derivatives assets represent a risk. To cater to different risk appetites, the pools are split into junior and senior tranches. Junior tranche participants receive higher yields but are exposed to more risk, as they absorb bad debt from the pool first. Senior tranche participants enjoy more security with lower yields, as they have priority in case of any defaults.

To protect senior tranches , we have implemented an insurance fund, which is acting ike an ultimate shield, funded by platform fees.

## Linear Interest Rate Model

The interest rate model manages liquidity risk in the protocol through user incentives to support liquidity:

When capital is available: low interest rates to encourage borrowing.

When capital is scarce: high interest rates to encourage repayments of debt and additional supplying.

Liquidity risk materialises when utilisation is high, and this becomes more problematic as the utilisation gets closer to 100%. To tailor the model to this constraint, the interest rate curve is split in two parts around an optimal utilisation rate $U_{optimal}$. Before $U_{optimal}$the slope is small, after it begins rising sharply.

$if \hspace{1mm} U \leq U_{optimal}: \hspace{1cm} R_t = R_0 + \frac{U_t}{U_{optimal}} R_{slope1}$

The borrow interest rates increase slowly with utilisation

$if \hspace{1mm} U > U_{optimal}: \hspace{1cm} R_t = R_0 + R_{slope1} + \frac{U_t-U_{optimal}}{1-U_{optimal}}R_{slope2}$

The borrow interest rates increase sharply with utilisation to above 50% APY if the liquidity is fully utilised.

## PID Interest Rate Model

Morphine's plan to transition from a linear interest rate model with a kink to a PID (Proportional-Integral-Derivative) controller rate model is driven by the desire to improve the platform's adaptability and responsiveness to market conditions. Here are some reasons behind this transition:

Enhanced adaptability: A PID controller rate model can better adapt to fluctuations in market conditions, such as varying demand for borrowing and lending, by continuously adjusting the interest rates in real-time. This adaptability can lead to a more balanced and efficient market on the platform.

Improved stability: By quickly reacting to changes in supply and demand, the PID controller rate model can help maintain the stability of the platform. It prevents sudden spikes or drops in interest rates that could otherwise disrupt the equilibrium between lenders and borrowers.

Optimized utilization: The PID controller model can optimize the utilization of the lending pools, ensuring that interest rates are set at a level that encourages borrowing without depleting the liquidity pools entirely.

Greater precision: The PID controller model offers more precise control over interest rates than a linear model with a kink. This increased precision can lead to better market efficiency and a more attractive platform for both lenders and borrowers.

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