# Interest Rate Model

The interest rate model is used to manage liquidity risk through user incentivizes to support liquidity:

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

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

Starfish uses the Jump Rate Model, which is an efficient measure to incentivise lenders to provide liquidity at times of high utilization. Liquidity risk materializes when utilization is high, in order to bring stability to interest rates, the interest rate curve is split into two slopes to cater Utilization rate when it approaches an optimal Uoptimal.

### Utilization Rate Model

The utilization ratio U for each market a unifies supply and demand ratio into a single variable:

Ua = Ba / (Da + Ba)

Two interest rate slopes (Rslope1 and Rslope2), parameters of the system, are used to compute the variable interest rate: Rslope1 is used when U < Uoptimal and Rslope2 when U âĨ Uoptimal.

The interest rate It follows the model:

If U < Uoptimal : I(t) = Io + Ua /Uoptimal â Rslope1

If U âĨ Uoptimal : I(t) = Io + Rslope1 + (Uaâ Uoptimal) / (1âUoptimal) â Rslope2

### Deposit APY Model

The borrow interest rates paid are distributed as yield for lenders 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, Da, is:

Da = Ua â Bt (1âIt)

Ua : the utilisation ratio.

Ba : the variable borrow rate.

Rt : the reserve factor.

### Borrow APY Model

Ba = 5% + Ua â 20%

### Base Interest Rate 5%

Utilization Rate(%) | Borrow Rate(%) | Deposit Rate(%) |
---|---|---|

1 | 5.12 | 0.04 |

5 | 5.62 | 0.2 |

10 | 6.23 | 0.44 |

15 | 6.85 | 0.72 |

20 | 7.46 | 1.04 |

25 | 8.08 | 1.41 |

30 | 8.69 | 1.82 |

35 | 9.31 | 2.28 |

40 | 9.92 | 2.78 |

45 | 10.54 | 3.32 |

50 | 11.15 | 3.9 |

55 | 11.77 | 4.53 |

60 | 12.38 | 5.2 |

65 | 13 | 5.92 |

70 | 27.29 | 13.37 |

75 | 41.57 | 21.82 |

80 | 55.86 | 31.28 |

85 | 70.14 | 41.73 |

90 | 84.43 | 53.19 |

95 | 98.71 | 65.64 |

100 | 113 | 79.1 |

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