The Formulas
This page shows the formulas used in mimo protocol.
Last updated
This page shows the formulas used in mimo protocol.
Last updated
In each trade, traders trade certain amount of a particular token for certain amount of another token with the price defined by a formula. There is no orderbook and waiting for fulfillment.
The formula that mimo uses is the famous that has been widely adopted by AMM based DEX, such as uniswap.
Assume that is the source token, and is the destination token. In mimo, , could be either IOTX or XRC20 tokens. Let , be X-token, Y-token in current liquidity pool, respectively.
Based on the famous AMM equation
where is a constant.
The product of and remains the same before and after trading. For details, please refer to vbuterin's post.
Let's further define , are how many X-tokens you want to pay, and how many Y-tokens you will get, respectively.
We'd like to know, the price based on or. IfgetInputPrice
denotes how many Y-Tokens (i.e. ) can be bought by selling a given ,
or in code,
or in code,
where /
in above equations denotes divToInteger
, which means divide with rounding to floor of the results.
or
in code,
Note that the price impact is always between -1
and 0
.
If there are no direct trading pairs between two tokens, like in V1 where we only support IOTX/token pairs, traders need to use one token, such as IOTX, as a bridge to trade among two tokens.
In this case, the price impact would be
or in code,
where
If getOutputPrice
denotes how many X-tokens is needed to buy Y-tokens,
In AMM, the price would change after each trade, , and the liquidity in the pool. The price impact is what traders want to know before the trade.
There are two ways of calculating price impact. It can be based on , or . One is based on input , one is based on output.