# Implied/Realised Vol ratio for negative rates?

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

• I have used shifted lognormal implied vols as as an alternative and this seems to be a decent enough workaround. Would still be interested if there's any other solution/suggestion. – oronimbus Jan 30 '20 at 17:38