Since options contracts are created by open interest in the contract, it is conceivable that the notional of the total options contracts can exceed the value of the underlying. If that happens, does the underlying become the derivative of the options?
This is more than just a theoretical question. I have started to see in some markets with large options open interest where the delta hedging of the options contracts start to impact the volatility of the underlying--particularly in high gamma/convexity contracts. Those that have negative gamma end up having to buy the underlying in large up moves and exacerbate the volatility on the upside. Conversely those with positive gamma do the opposite in large down moves. In these markets, would we see larger smiles?
Have there been any studies of this feedback phenomenon? Any literature recommendations would be appreciated.