Does vanilla put call parity imply smirks are bounded on the implied volatility surface?When testing extreme moves in a smirked surface, parity appears to break down, creating arbitrage potential until reverting to this 'implied bound'. I havn't been able to find any specific literature on this. I do recall extreme smirks in some commodity markets (Sugar), which may have been an opportunity missed. Or am I missing something here?

No.Put call parity just tells you that the implied vol of the vanilla European put and call with the same strike must be the same, absent transaction costs.There are bounds on the smile shape, but they come from requiring absence of arbitrage across different strikes: call prices must be decreasing as a function of the strike (or you could buy a call, sell one for a higher strike for money money, pocket the difference and have a non-zero payoff), and they must be concave upwards (in math terms, the PDF is the second derivative of the price, and it has to be positive).

THEORY: No.At each date t, strike K, and expiry date T, there can be two European options: one is a call and the other is a put.The two options should generate the same implied volatility value to exclude arbitrage.1 - Recall put-call parity: c − p = er (T−t)(F − K).2 - The difference between the call and the put at the same (t,K,T) is the forward value.The forward value does not depend on (i) model assumptions, (ii) time value, or (iii) implied volatility.PRACTICE: Yes (you´re so right, and there´s hardly any literature because you spotted a major source of arb!).Broker-Dealer making markets on "Securitised Derivatives" cannot guarantee holding these relations all-of-time, for all-of-the-options, since as "liquidity providers" they must sometimes slip over and disrupt parity by taking the other side of a client´s trade ( ie, in the absence of a market, you have to provide one as a broker-dealer ). During these events, market-makers are usually arbed against, there are in fact, funds specialized in this line of arbitrage, usually happening off exchange trading hours, ie, when the broker-dealer is left alone.

Thanks Gents, I agree with you - ATM vols are the same given put call parity. The story becomes different when moving to the wings. Short a 90 delta call and long a 10 delta put implies a smirk would be bounded with put call parity. Appreciate your help.FH

Not sure I understand why put/call parity is different in the wings, liquidity/transaction cost/bid-ask spread issues aside. Why does, and what do you mean by, "Short a 90 delta call and long a 10 delta put implies a smirk would be bounded with put call parity"?