When you buy an asset the price you pay is currently highest amongst other buyers and conversely the seller you buy from will offer the lowest price amongst other sellers.
There's this tiny overlap, where you and a seller agree to the exchange because you believe the asset's worth a little more and the seller a little less.
At that instant you're part of a unique pairing; the trade's details are logged noting the exchange; and the market trundles on.
That throws up a few interesting ideas.
Firstly, at that moment you value the asset above every other buyer. Perhaps you know something everyone else does not, or perhaps you've bought something everyone else is happy to avoid.
Secondly. By tweaking the way the market worked just a little something very interesting would occur.
If the winning buyer bid but only had to pay the second highest bid, all buyer's best strategic bids would be to just report their valuation truthfully.
So rather than just being able to tell when the bid-ask spread has been broached over time when a buyer and seller's valuations overlap; we would have a complete view of every market participant's valuations over time.
Instead of measuring volatility over time, you could now instantaneously take a snapshot of how all market participant's valuations are dispersed.