Crypto instability is largely caused by a low population of investors or holders. As the quantity of "players" in a true (i.e., non-manipulated) market increase, the stability will increase naturally, in direct proportion. That's the theory anyway. :~)
Currently, there are no Fiat Markets. They are all being 'centrally' controlled and thus artificially manipulated.
All markets (Stock, Bonds, Fiat Currencies, Gold, Silver, Property, Commodities, etc.) are being manipulated ... mostly by the ESF (Exchange Stability Fund).