If the Black model is correct, what should be the relation between the strike price on options on a futures contract (such as on natural gas future) and the volatilities implied by the prices of these options? What relation between strike and implied volatility is typically observed in reality? Provide a brief explanation of what can account for the observed strike-implied volatility relation. Why might the “smile” “smirk” towards the “call wing”? Why might it “smirk” towards the put wing?
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