# Interest Rate Model

Mitigating liquidity risk through the borrow interest rate model

Vinci’s interest rate strategy is calibrated to manage liquidity risk and optimise utilisation. The borrow interest rates come from the $U$.

Each currency reserve is characterised by its utilisation rate $U$ :

$U \hspace{1mm} = \hspace{1mm} Total Borrows \hspace{2mm} / \hspace{2mm}Total Liquidity$

$U$monitors which share of the reserve’s total capital is borrowed at time $t$.

$U$is an indicator of the availability of capital in the pool. The interest rate model is used to manage liquidity risk through user incentivises to support liquidity:

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

When capital is scarce: high interest rates to encourage repayments of loans and additional deposits.

## Interest Rate Model

Liquidity risk materialises when utilisation is high, its becomes more problematic as $U$ 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 starts rising sharply.

The interest rate$R_t$follows the model:

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

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

The resulting actual borrow rate is:

$Actual APY = (1+Theoretical APY/secsperyear)^{secsperyear}-1$

When $U < U_{optimal}$ the borrow interest rates increase slowly with utilisation

When $U \geq U_{optimal}$ the borrow interest rates increase sharply with utilisation to above 50% APY if the liquidity is fully utilised.

## Deposit APY

The borrow interest rates paid are distributed as yield for vToken holders who have deposited in the protocol, excluding a share of yields sent to the ecosystem reserve defined by the reserve factor. This interest rate is paid on the capital that is lent out then shared among all the liquidity providers. The deposit APY, $D_t$, is:

$D_t = U_t I_t(1-R_t)$

$U_t$, the utilisation ratio

$I_t$, the borrow interest rate

$R_t$, the reserve factor

### Reserve Factor

The reserve factor allocates a share of the protocol's interests to a collector contract as reserve for the ecosystem incentives.

## Interest Rate Model Parameters

NFT Collection | U_optimal | Base | Slope 1 | Slope 2 | Reserve Factor |
---|---|---|---|---|---|

CryptoPunks | 45% | 1% | 4% | 80% | 30% |

Bored Ape Yacht Club | 45% | 1% | 4% | 80% | 30% |

Mutant Ape Yacht Club | 45% | 1% | 4% | 80% | 30% |

Moonbirds | 45% | 1.5% | 6% | 100% | 30% |

Doodles | 45% | 1.5% | 6% | 100% | 30% |

Azuki | 45% | 1.5% | 6% | 100% | 30% |

CLONE X | 45% | 1.5% | 6% | 100% | 30% |

## Interest Rate Curve

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