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
UU
.
Each currency reserve is characterised by its utilisation rate
UU
:
U=TotalBorrows/TotalLiquidityU \hspace{1mm} = \hspace{1mm} Total Borrows \hspace{2mm} / \hspace{2mm}Total Liquidity
UU
monitors which share of the reserve’s total capital is borrowed at time
tt
.
UU
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.

Liquidity risk materialises when utilisation is high, its becomes more problematic as
UU
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
UoptimalU_{optimal}
. Before
UoptimalU_{optimal}
the slope is small, after it starts rising sharply.
The interest rate
RtR_t
follows the model:
ifU<Uoptimal:Rt=R0+UtUoptimalRslope1if \hspace{1mm} U < U_{optimal}: \hspace{1cm} R_t = R_0 + \frac{U_t}{U_{optimal}} R_{slope1}
ifUUoptimal:Rt=R0+Rslope1+UtUoptimal1UoptimalRslope2if \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:
ActualAPY=(1+TheoreticalAPY/secsperyear)secsperyear1Actual APY = (1+Theoretical APY/secsperyear)^{secsperyear}-1
  • When
    U<UoptimalU < U_{optimal}
    the borrow interest rates increase slowly with utilisation
  • When
    UUoptimalU \geq U_{optimal}
    the borrow interest rates increase sharply with utilisation to above 50% APY if the liquidity is fully utilised.

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,
DtD_t
, is:
Dt=UtIt(1Rt)D_t = U_t I_t(1-R_t)
  • UtU_t
    , the utilisation ratio
  • ItI_t
    , the borrow interest rate
  • RtR_t
    , the reserve factor

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

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%

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Interest Rate Model
Deposit APY
Reserve Factor
Interest Rate Model Parameters
Interest Rate Curve