I encountered this question: "A trader observed that the implied vol of OTM calls and puts are higher than that of ATM option, what is the best strategy among: Calendar Spread, Bull Spread, Bear Spread and Butterfly ?"
Only if other traders didn't knew this volatility shape and were using the regular Black-Scholes pricing model, could the trader capitalize on this discovery. Then, the calls with high strike price would be under-priced and the puts with low strike price would be also under-priced. The trader then would want to buy lots of calls with high strike price and lots of puts with low strike price. Besides, none of the payoffs above take advantage of this property. (Maybe shorting a butterfly spread?)