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?
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.
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.