Asset price inflation during the boom is driven by Fed induced monetary inflation and credit expansion. So with or without modern derivatives, we get the boom-bust cycle, e.g. the roaring twenties followed by the Great Depression.
Moreover, derivatives are ancient, not modern and yet, business cycles arise in the 18th and 19th century.
Finally, the take-off of financial markets occurred during the 19th century, coincident with the greater centralization of monetary inflation and credit expansion and greater regulatory interference of financial markets by the government. Scroll down to the charts starting on page 52: