One feature that come together with Liquid Pylon Vault is that we also provide best rate deposit to the vault using only UST.
Most of the time, we can get bPsiDP-24m from Terraswap at a discount rate, however, if we swap too many tokens in one transaction, the price of bPsiDP-24m might go above $1.
To ensure that you will always get the best rate for their deposit, we need best rate deposit mechanism for this vault.
Solution overview is simple:
- We will find maximum UST amount (Optimal amount) to swap at Terraswap to get bPsiDP-24m with the rate less than $1 first.
- Then the remaining amount will deposit directly via Pylon gateway, which rate is fixed at $1.
Here are the implementation details (Warning: math ahead!):
In Terraswap, we cannot swap directly from UST to bPsiDP-24m. We need to swap in 2 steps:
- From UST to Psi
- Then Psi to bPsiDP-24m
For Psi-UST pool: finding UST for a Psi amount
Terraswap swap rate is using this formula
From (1), this is the formula for swapping UST to Psi
From (2), we can shuffle variable to find UST amount
From (3), we can simplify to
For bPsiDP-Psi pool: finding bPsiDP for a Psi amount
This step is easy, from (1), we can get to this formula
And from (5), we can simplify to
Mix 2 pools together
Given that UST amount equal to bPsiDP amount, from (4) and (6), we can come to this formula
Let’s replace Psi amount with X
Now let’s move everything to one side
And simplify to
From here, we can apply quadratic formula
After apply, it will transform into
And simplify into
Now we can find optimal Psi amount. After we get X, use equation (4), we can find optimal UST amount
Here is pseudo code to find optimal UST amount
With best rate deposit to Liquid Pylon Vault, you can simply deposit UST to the vault and we will make sure that you will get the best rate without a hassle of going too many different apps or comparing different exchange rates.