Realized Swaption Volatility as Standard Deviation of Yield Changes

Summary

The document addresses how to compare implied and realized volatility for swaptions when rates approach or fall below zero. The questioner uses broker-quoted normal at-the-money volatility, expressed in basis points, and finds that converting percentage returns into basis-point volatility by scaling with the rate level becomes unstable near zero. Log returns are also unsuitable for negative rates.

The answer’s practical guidance is to calculate realized basis-point volatility directly from the standard deviation of absolute yield changes over the chosen horizon. This measure is based on rate movements rather than the rate level, so it remains usable when rates are near zero or negative. The source gives no specific sampling window, annualization convention, or comparison of estimators; those choices still need to match the implied-volatility quote and intended horizon.

Key ideas

• Normal swaption volatility is quoted in basis-point terms, so realized volatility should use compatible units.
• Compute realized basis-point volatility from the standard deviation of absolute yield changes.
• Scaling percentage volatility by the rate level becomes unstable as rates approach zero.
• The answer does not prescribe a sampling horizon or annualization convention, which should be chosen consistently with the implied quote.

Tags

# Implied/Realised Vol ratio for negative rates?


# 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

## Answer by VolGuy (score 1)

https://quant.stackexchange.com/a/57631

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.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.