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If you think volatility is too cheap, how do you decide if an ATM call or an upside call (which trades at lower vol because of skew) is better?

Let's say you have a $100 stock. You think the stock will move on a 20 volatility.

You have 2 choices:

Buy the 100 strike call for an 18 implied volatility.

Buy the 120 strike call for an implied volatility of 16.

How does one intuitively go about assessing what the better option is? Purely saying, hey 16 is a lower implied volatility so it's better seems way too simple. Any thoughts/ideas? What other things should we know?

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  • $\begingroup$ First things that'd come to my mind are what are the delta-equivalent vega/gamma profiles of the the 2 options. You want to be delta-neutral, long gamma, long vega to run this trade. Would also be interesting to see what the best combo of the 2 options would give, eg what is the delta-equivalent vega/gamma position of buying the 100 strike vs selling the 120 strike for example or vice versa $\endgroup$ – Mehness Jun 8 '18 at 22:53
  • $\begingroup$ So in short, u think realised will be high, u want to stay delta neutral whether you're hedging option with delta or option with option, you want to be long gamma, and pbbly long vega - a quick spreadsheet calc to term of the profiles of those greeks to term or unwind horizon would be the first step. Then scenario analysis. You might like the delta - neutral implied compression trade too :) (sorry, not your qn but the possibilities are several!) $\endgroup$ – Mehness Jun 8 '18 at 22:55
  • $\begingroup$ but anyway sticking to your actual question (!) you have to know at the very least how your gamma and delta vs option are going to perform over time to weigh up the trades. $\endgroup$ – Mehness Jun 8 '18 at 23:04
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First of all, you should understand where the IVs are coming from and the assumptions made in the model to derive the values.

IVs are solved through option pricing models by the given market prices of the options. Many of the option pricing models assume underlying securities are lognormally distributed, for example BS model. However, the market participants disagree on that. Volatility smiles(smirks) actually represent how market participants disagree on the model, because if the market prices of options are exactly same as BS model, the IVs smiles are actually a flat line.

So buying an option from a strike with lower IV doesn't mean you get a "better deal", because the distribution of underlying might be totally different from the model used to solve IV. Also, options prices(also IVs) are determined by many factors such as type of securities(FX are more like smile but equities indexes are more like smirk), supply-demand, market scenarios and idiosyncratic events. So staticly look at the IV skew doesn't tell you if it's truely, and relatively, cheap or expensive.

However, looking at the dynamics of skew change might tell you the option is relatively cheap or expensive comparing other strikes. Lots of hedge funds' option groups are actually trading for skews. There are a few skew trading strategies you can easily find online

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Here are two questions you should ask: (1) looking at historical information, how cheap has the 20pct otm call traded at versus the ATM ? Is the 2 point discount high or low versus history (2) what do you think will happen to realized vol if the stock goes to 120? The market, through the skew pricing, is saying it will go down significantly. If you do not believe that, collecting the 2 point discount may be a good idea.

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