Yes. People determine whatever value they want for Bitcoin. Since there's no central issuer or authority, Bitcoin is free from any standard valuation. It's based on belief and its underlying technology. There's no other explanation, considering that Bitcoin is just programmable money composed of ones and zeros. If we were to base our valuation on this, then Bitcoin would be worthless. However, because Bitcoin has managed to bring a technology which provides transparency and prevent double spending, it has an inherent value provided by its users.
And that also explains why Bitcoin is a volatile cryptocurrency, because within any given day, people can either recognize it as a valuable cryptocurrency, or all the contrary. Despite this, I believe that Bitcoin will always be a valuable cryptocurrency because of its limited supply, deflationary model, and unparalleled security unlike any other cryptocurrency in existence. Therefore, Bitcoin is backed and will always be backed by its users, which is quite an advantage when compared against traditional fiat currencies. Just my opinion