If I'm pricing options using calendar days(365), then I should even annualize realised volatility by multiplying 18.8(√256) instead of 16 (√256, approx trading days). In order to compare the VRP ratio on same scale, am I right?
You should not annualize by sqrt(365). Once annualized they are in the same units. The issue is that IVs from any vendor are wrong. This has to do with assumptions about how variance is allocated across a calendar. A 365 day model thinks every day is equal. A business day trading model thinks the weekends are worthless. Both assumptions generate incorrect IVs.
However, incorrect IVs are not too misleading when you are looking cross-sectionally (ie relatively) if you compare assets with the same times to expiry. It gets trickier when you compare IVs cross-asset (when expiration times are not all 4pm eastern)
I should make a video or write up explaining how to think of this and why
(annualized numbers are like 9" pizza pies...it doesn't matter how you cut up the slices...but IVs differ because the time remaining will disagree across models. So the problem isn't in comparing IV vs RV it's that the IV itself depends on the time to expiry and not everyone agrees on that number because you how you cut the pie up)
A hint here is that both a 365 day and 252 day option model will give the same IV on Jan 1 for a given 1 year straddle price. But as soon as you are 1 day into the year, the IVs will start disagreeing for the same given straddle price
There is no such thing as a fair football line in which the Jets are only getting seven points
If I'm pricing options using calendar days(365), then I should even annualize realised volatility by multiplying 18.8(√256) instead of 16 (√256, approx trading days). In order to compare the VRP ratio on same scale, am I right?
19.1(√365)
You should not annualize by sqrt(365). Once annualized they are in the same units. The issue is that IVs from any vendor are wrong. This has to do with assumptions about how variance is allocated across a calendar. A 365 day model thinks every day is equal. A business day trading model thinks the weekends are worthless. Both assumptions generate incorrect IVs.
However, incorrect IVs are not too misleading when you are looking cross-sectionally (ie relatively) if you compare assets with the same times to expiry. It gets trickier when you compare IVs cross-asset (when expiration times are not all 4pm eastern)
I should make a video or write up explaining how to think of this and why
(annualized numbers are like 9" pizza pies...it doesn't matter how you cut up the slices...but IVs differ because the time remaining will disagree across models. So the problem isn't in comparing IV vs RV it's that the IV itself depends on the time to expiry and not everyone agrees on that number because you how you cut the pie up)
A hint here is that both a 365 day and 252 day option model will give the same IV on Jan 1 for a given 1 year straddle price. But as soon as you are 1 day into the year, the IVs will start disagreeing for the same given straddle price
Thank you for the explanation!!