Nope, there is a whole legal/financial/governmental/military structure backing fiat currency. There is nothing like that backing BTC. By the way, stocks and bonds do not have exactly the value that people place on it. It is not a financial instrument which value is defined only by speculation.
Actually, it IS the value that people place on all these things. However, it isn't always direct value.
We wouldn't have a military if people didn't place trust in government officials to provide a military. So, indirectly, it is the value that people place on the military.
Now that people can see more and more how the banks and government and the military are NOT doing what they want, the people are turning to Bitcoin to overcome the problems that they see in the system.
It all has to do with the value people place on everything.