Calculation Methodologies

Exchange Rate Calculation
We use the formula below to calculate the exchange rate:
rcv = a * B / (A + a) 
rcv_net = rcv * (1 - fee) 
where a is the amount of token X sent by swapper and A is the total amount of tokens X in the pool before the swap
Then, the exchange rate is simply lim a -> 0 (rcv / a) which equates to B/A. 
In terms of how much a user shall receive b given a supplied:
b = a * B / (A + a) * (1 - fee) 
Asset Price Calculation
Internally, a fixed pricing algorithm is used to calculate the spot $USD price of assets swapped via the Pact AMM pools. To achieve this the algorithm tracks every SWAP pool call, distinguishing between swaps with: 
Stablecoin Swaps (USDT or USDC) and;
General Swaps (all other assets)
Stablecoin Swaps
For swaps with either USDT or USDC (let’s call them STABLE), it assumes the stablecoin has price of $1 and uses the following formula:
priceasset=priceSTABLE∗totalSTABLE∗10decimalsassettotalSTABLE∗10decimalsSTABLEprice_{asset} = \frac{price_{STABLE} * total_{STABLE} * 10 ^{decimals_{asset}}}{total_{STABLE}  *10 ^{decimals_{STABLE}} }priceasset​=totalSTABLE​∗10decimalsSTABLE​priceSTABLE​∗totalSTABLE​∗10decimalsasset​​
​priceSTABLEprice_{STABLE}priceSTABLE​
 is the price of STABLE (1$) 
​totalSTABLEtotal_{STABLE}totalSTABLE​
 is a total number of STABLE in pool after SWAP
​totalassettotal_{asset}totalasset​
 is a total number of asset in pool after SWAP
​decimalsassetdecimals_{asset}decimalsasset​
 asset’s decimals 
​decimalsSTABLEdecimals_{STABLE}decimalsSTABLE​
 STABLE’s decimals
General Swaps
For swaps between other assets, the price will only be calculated if there has been a prior SWAP app call to the STABLE/A or STABLE/B pool, because in this case A/B already have an implicit price calculated. From here, the formula is similar:
priceA=priceB∗totalB∗10decimalsAtotalA∗10decimalsBprice_A=\frac{price_B*total_B * 10^{decimals_A}}{total_A * 10^{decimals_B}}priceA​=totalA​∗10decimalsB​priceB​∗totalB​∗10decimalsA​​
​priceBprice_BpriceB​
 is the price of B calculated from SWAP app call in STABLE/B pool
​totalAtotal_AtotalA​
 is a total number of A in pool after SWAP
​totalBtotal_BtotalB​
 is a total number of B in pool after SWAP
​decimalsAdecimals_AdecimalsA​
is A’s decimals
​decimalsBdecimals_BdecimalsB​
is B’s decimals
Note: If there are no STABLE/A or STABLE/B pools, then the price won't be calculated and the value will be set to "-".
Last modified 8mo ago