You are right. Bitcoin is a crypto currency how it can be stabble where fiat's price ups and downs against another fiat currency. For example if you can see today 120$ = 100 euro than so it will be higher or lower.
Bitcoin's price is not determined by anything. If you decide to buy it at 1$ then its price is 1$. What we see in exchanges as buy and sell walls are just because people are ordering coins at those prices. Nobody wants to sell below the market price which is the current highest bid and thus the price inflates are become big. But if you wish you could also sell it at lower price at your one dealings. There would noting keeping the price stable here.
It is not like gold where a piece of gold is pledged to every ETF of gold.