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Converting Annual and Daily Basis-Point Volatility

Article Quant Q&A · Author: GChan
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Summary

The document addresses volatility conventions used in interest rate options, where volatility may be quoted as a percentage, annual basis-point volatility, or daily basis-point volatility. Its answer identifies the latter two abbreviations and gives approximate conversions: daily basis-point volatility is annual basis-point volatility divided by the square root of 252 trading days, while lognormal volatility is annual basis-point volatility divided by the forward rate.

These relationships help translate between quoting formats, but the explanation is brief. It does not define the precise market convention for each quote, discuss units or compounding assumptions, or specify adjustments that might be needed for a particular product. The conversion to lognormal volatility is therefore best read as an approximation tied to the stated forward rate, rather than a complete pricing prescription. No worked example or market data is provided.

Key ideas

  • Annual basis-point volatility and daily basis-point volatility are alternative ways to express rate volatility.
  • Daily basis-point volatility is approximated by dividing annual basis-point volatility by the square root of 252.
  • Lognormal volatility is approximated by dividing annual basis-point volatility by the forward rate.
  • The stated conversions are concise approximations and do not cover product-specific conventions or assumptions.

Tags

OptionsFixed incomeVolatilityDerivatives pricing
Full text
# Different volatility convention


# Different volatility convention












In listed option's world, sometimes I see someone put different vols interchargablly, e.g. 6.7% Vol or 171 abpv or 11 dbpv may anyone elaborate each jargon in some detail, and how and when should they be used? Also are there any formula to quickly derive one another? Thanks.

## Answer by dm63 (score 3)

https://quant.stackexchange.com/a/76106

I’ve never seen those on Bberg but I’m sure they stand for annual basis point vol and daily basis point vol respectively. This is how most people look at interest rate options. You can also look at lognormal vol but most people don’t. The approximate relationships between them :$$ DBpv = abpv/ sqrt (252). $$ And $$ Logvol = abpv/ forward rate $$

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