Hi,assume we have to price this payoff with terminal value : Max( Max( Sa,Sb)-Strike,0).the question is: Intuitivly How the skew will impact the price of this option in the following cases ?case 1 : Skew of the asset Sa increases and the skew of the asset Sb will stays the same.case 2 : Skew of the asset Sa increases and the skew of the asset Sb increases.case 3 : Skew of the asset Sa increases and the skew of the asset Sb decreases. Thank you in advance

This is a good interview question, given that I have heard two different answers to the question of how skew impacts this structure!One way to look at it is that initially, this is a lot like the "best of 2 calls": max(call on S1, call on S2).So you can sort of think of hedging the whole thing using a call on S1 and call on S2 (in some ratio, maybe keeping vega neutral).Then it depends upon how you define "skew". If changing the skew has zero effect on the ATMF options and this is struck ATMF on day one, then the "underlying options" (vanilla calls on S1 and S2) will be unaffected. But their hedge ratio might be affected. If the strike is not ATMF, then skew would have a direct effect on the "underlying options". If they have low strikes, increasing skew would increase their value. If they have high strikes it would decrease their value. So this part of the effect could have either sign.To see another important effect, look at this as a call on a "funny underlying". The funny underlying is max(S1,S2). Now you can ask yourself how the "best-of-2" forward is affected by skew. I would expect that increasing the skew would decrease the chances of a big upward move, so the worst-of-2 forward should go down. This should mean that your hedge ratio for the two underlying options would decrease, and since the value of the replicating portfolio decreases, the value of the derivative should decrease.So it is a balance between competing effects, and I would say "it depends upon the strike and current moneyness(es)".Next you can ask about the situation in which time has passed, and maybe S2 >> S1. In that case it should act pretty much like a call on S2. The sign of the effect would then depend upon whether the call on S2 is ITM or OTM!It would be interesting to set up the derivative model fully with skew and calculate the answer!