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Are there rules of thumbs/models that you could use to develop intuition for when skew is cheap or expensive? From what I gather, volatility is a number that is backed out of price in a sense, "the wrong number to get the right answer". But then someone has to set the price, they have a sense of what the correct "skew" is, and I'm trying to understand some intuitive way of understanding.

If for instance in a 100 stock ATM vol is trading at 35, and the stock has historically moved at 30 vol, you can have some sense that 35 is expensive. However, if the 80 strike was quoted at 35 volatility, is that cheap or expensive? How would one go about trying to answer this question?

How did traders use to price skew before we had complicated models that went beyond B/S?

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  • $\begingroup$ I think this is up to experience basically. There isn't a model which is going to tell you whether skew is cheap/expensive, because skew is an empirical phenomenon caused by supply/demand dynamics of options. There are even asset classes for which there's a skew instead of a smile, there is no much theoretical justification for that really. Best thing is to investigate historical data on vol curves to get an intuition, and going forward maybe check daily, weekly how the curve has evolved to get a feel as @noob2 suggest. $\endgroup$
    – Daneel Olivaw
    Apr 13, 2020 at 14:04
  • $\begingroup$ @DaneelOlivaw yeah, that makes sense. I'm just trying to figure out a way to make skew "real". You can trade realized vs IV in a relatively simple way following simple rules, trading "skew" which you implicitly are anytime you trade a non ATM option so it's just confusing af. The only thing I can really think of are just the hard arbitrage limits but those are so wide as to be almost meaningless $\endgroup$
    – user3002540
    Apr 13, 2020 at 20:59
  • $\begingroup$ There are some common measures you can use, check Wikipedia. $\endgroup$
    – Daneel Olivaw
    Apr 13, 2020 at 21:20
  • $\begingroup$ @DaneelOlivaw thanks, I'll check those out. It seems local volatility is probably the "right" answer in a way to what I'm looking for, thanks $\endgroup$
    – user3002540
    Apr 14, 2020 at 0:57

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For example you could ask yourself what the realized volatility will be if the stock were to be at 80 at some time in the future. If the answer is ‘much higher than the realized volatility when the stock is at 100’, then that would be a reason why the implied vol of the 80 strike is higher than the at the money. The reason for this is that options derive much of their value from the expected volatility in the region of the strike price. Thinking about this strike versus realized volatility dependence is a key intuition for pricing skew in various markets.

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  • $\begingroup$ There's lots of factors though right? One would have to figure in the probability of the stock first getting in that region right? So if I'm looking at the 10% moneyness put, it maybe in that world the stock is almost bankrupt and so volatility is very high but a very small chance of getting there has to dent the implied vol at time zero today right? $\endgroup$
    – user3002540
    Apr 13, 2020 at 1:18
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Another example of a thing you can do. Every day I receive a chart showing the skew, i.e the IV versus strike for S&P options. Don't throw all those out the next day, save a few of them and tape them to your cubicle wall. That way you can develop a feel for what the skew has looked like in various historical circumstances, in quiet periods and in stressed periods (like on March 23, 2020), how it changes, what is normal, etc. Sometimes this goes by the fancy name of "stress testing" or "historical episode testing".

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  • $\begingroup$ Please say this isn't how you actually operate in this day and age! $\endgroup$
    – will
    Apr 13, 2020 at 17:20
  • $\begingroup$ This is interesting, I see your point, seeing how the curve was in the past. I guess the real question is how you test if those past curves were "correct". You can judge whether ATM vol was "correct" in a way or not based on realized, it seems to be come less clear for non ATM $\endgroup$
    – user3002540
    Apr 13, 2020 at 21:06

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