Rebalance Mechanism

To facilitate seamless and successful token swaps between liquidity pools, TOKI ensures adequate balances in each pool. Swaps can shift balances, depleting destination chain pools while increasing source chain pools. To address this, TOKI employs the rebalance mechanism that incentivizes swaps that restore balance and discourages actions that would deplete pool reserves.

The rebalance fees and bonus are set as follows:

• Current balance: $b$

• Ideal balance: $B$

• Transaction size: $t$

Rebalance Fee and Bonus	Condition
0	$b-t ≥ \delta_1B$
$\frac{\lambda_1}{(\delta_1-\delta_2) B} (\delta_1 B - b+t)$	$\delta_2 B ≤b-t<\delta_1 B$
$\lambda_1 + \frac{\lambda_2}{(\delta_1-\delta_2) B} (\delta_2 B - b+t)$	$b-t < \delta_2B$

Hyperparameters are set as follows:

• $\lambda_1$ : 40bps

• $\lambda_2$: 99.54%

• $\delta_1$ : 60%

• $\delta_2$ : 5%

If the pool on the source chain is in deficit, users will receive the rebalance bonus capped at the protocol fee to ensure the user does not generate a surplus.

On the other hand, if the pool on the destination chain is in deficit, the rebalance fee might be added to the TOKI Fee paid by the user.

(*1) Deficit: This occurs when the amount of stable tokens held by the pool is less than the total amount of stable tokens provided as liquidity to the pool.