Implied/Realised Vol ratio for negative rates?

External question — Quantitative Finance Stack Exchange Author: oronimbus Original post: https://quant.stackexchange.com/questions/50882 License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/ Adaptation: HTML converted to plain text; contact email addresses removed. I'm trying to calculate the implied vs realised vol ratio for different swaptions across major currencies. This works fine for the likes of USD and GBP as rates are positive. However I'm struggling with adapting this to EUR. For the implied vol data I can directly use the quoted normal ATM bpVol by a broker. For the realised volatility however, I'm calculating the basis point equivalent using $\sigma_N = \sigma_R \cdot \sqrt{252} \cdot F_{ATM}$ where $\sigma_R$ is just the stdev over some period. For the standard deviation I can either use daily percentage returns or absolute differences as log-returns obviously won't work. Now every time rates start to approach zero (and dip below) the I/R-vol ratio starts to go haywire: My questions are: is my approach wrong and is there any other way to get a bpVol equivalent for realised volatility? The only other solution that came to mind is using shifted Black volatilities (I need to check if I can get those...) and %-realised vol instead. Thanks

External answer — Quantitative Finance Stack Exchange Author: VolGuy Original post: https://quant.stackexchange.com/a/57631 License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/ Adaptation: HTML converted to plain text; contact email addresses removed. realized bp vol is simply standard deviation of abs changes in yields over the horizon you are looking at. Level of rates won't matter.