The current market price is the average market price of the asset at the time the Atomic Swap Quote is initiated. Note that the price gets "locked" only after you've selected Initiate Atomic Swap Quote.
The average market price might go through small to major fluctuations from the point of the market price lock to when the swap goes live, depending on how long it takes for your approval policy to be met. Note that (depending on your Approvers) your approval policy might not be met within the following 24 hours (the quote is rendered unsuccessful after being unapproved for this long).