Scalar rates

Scalar rates are used to parameterize Notional’s AMM and impact the steepness of the AMM curves.

Visual representation of different scalar values (keeping the anchor rate constant)

Impact of scalar rates on slippage

As showcased above, high scalar value AMM curves are flatter and exhibit lower interest rate sensitivity and lower slippage. On the contrary, low scalar value AMM curves are steeper, more interest rate sensitive and are subject to higher slippage.

Selected parameters

We selected the following scalar rates in conjunction with the anchor rates (see Anchor rates section) with the objective of:

• minimizing slippage for the 2% to 10% (stablecoins) and 0% to 7% (crypto assets) trading interest rate ranges;

• enabling permissive AMM curves with interest rate ranges of 0% to ~20%. These wide ranges aim to accommodate extreme market conditions and high redeemability for nTokens as we feel quite confident that end-users would actively lend at fixed rates of 15 to 20%;

• ensuring that the selected leverage thresholds are set at implied interest rates of̴ ~ 10%(stablecoins) and ~7% (crypto assets) (see the nToken Leverage threshold section).

Based on these conditions we selected the following scalar rates:

Cash Group	Scalar (3 month)	Scalar (6 month)	Scalar (1 year)
Stablecoins
USDC	48	47	45
DAI	48	47	45
Crypto assets
ETH	45	45	NA
WBTC	66	66	NA