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Let's say a trading firm wants to buy $5 MIL worth of SYN (https://www.coingecko.com/en/coins/synapse) in Uniswap V3 pools. SYN currently has a market cap of $135 MIL. I know how to calculate the price impact if it is to purchase it all at once.

But in practice, to minimize price impact, one would split this 5 MIL into x number of smaller purchases over y number of days. How can I simulate this so I can find the optimal x and y (aka maximize the number of SYN tokens with $5 MIL), while using actual historical price and liquidity pool data at Uniswap V3?

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