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After reading this and this, I still don't understand the reason for why options are quoted in terms of implied volatilities. My question is: can somebody give an example that shows the value/usefulness of using IV instead of option's price as a quote? In my understanding there is one-to-one correspondence between the two. Assume I give you the price instead of IV, what exactly will you not be able to do?

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  • $\begingroup$ Not all markets quote prices in terms of implied vol, could you clarify what market does this relate to please? $\endgroup$ Oct 17, 2020 at 22:36
  • $\begingroup$ Bloomberg database quotes options in terms of implied volatilities. $\endgroup$
    – Qwerty
    Oct 17, 2020 at 22:41
  • $\begingroup$ IV is often a valuation metric: traders compare IV to historical IV to determine whether an option is overvalued or undervalued; they may also compare the difference between IV and historical volatility to the same effect. Though the literature is clear that there is no clear mathematical relationship between IV and historical volatility, the extent to which one exceeds the other may be a useful metric in determining a “bargain”. Alternatively, the price is what it is, but it doesn’t tell you whether the option is expensive or cheap; IV helps you do that. $\endgroup$
    – CasusBelli
    Oct 17, 2020 at 23:13

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The reason for people quoting in IV is because spot is moving! If someone asks for a quote in 50 delta SPX, that will move by the millisecond. But if you just quote it in vol terms then that is pretty static. It just makes getting a trade done simpler.

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IV quotes let you compare prices of options on the same underlying with different strikes, expirations and types.

It is hard to say if 2.50 for 200@45dte is more or less than 3.70 for 150@90dte. Their implied volatility is directly comparable.

Some claim that you can also compare IVs for options with different underlyings but I’m less sure about that.

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  • $\begingroup$ Thank you! Interesting! So, what would you say if you have two options with different prices and different parameters, BUT having the same implied volatility? $\endgroup$
    – Qwerty
    Oct 17, 2020 at 23:41
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    $\begingroup$ If we ignore the smile, then it means that options are valued the same. I.e. if you have a reason to think that one is undervalued, you should conclude from your pricing model that the other is undervalued too. $\endgroup$
    – mikea
    Oct 17, 2020 at 23:49
  • $\begingroup$ ...two options with different prices and different parameters, BUT having the same implied volatility. How come the options are valued the same? Prices are different. $\endgroup$
    – Qwerty
    Oct 17, 2020 at 23:54
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    $\begingroup$ @Qwerty: you can break down the option price into two distict components: (i) intrinsic value (which is just spot - strike for calls, and strike - spot for puts), (ii) the "optionality" value. If two options on the same underlying have the same IV and maturity but different price, you could conclude that their "optionality" value is valued the same. The difference in price would be due to the difference in their intrinsic values (i.e. different strikes, i.e. one option would be more in the money than the other). $\endgroup$ Oct 18, 2020 at 9:23
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I could also add that options at more extreme strikes can be very insensitive to the volatility. Unless you use a ridiculous number of decimals for the option prices in that situation, those prices would then look the same on the market screen, while the volatilities for the options might differ more substantially. So for this numerical reason it is also more practical to give the volatilities instead of the option prices.

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