Choosing Normal or Black Volatility for Interest Rate Caps

Summary

The document discusses which volatility convention to use when deriving forward volatilities from cap prices. Its central point is that the appropriate model depends on the currency and rate environment. For currencies such as EUR or CHF, negative rates and negative-strike floors can make Black volatility unusable across parts of the surface; the response says Black vols may be unavailable for some expiries. Normal (Bachelier) volatility is presented as a practical alternative, since caps and floors in many markets are quoted in normal basis-point volatility or forward-premium terms.

For discounting, the answer describes OIS as the market standard and recommends building a Normal(OIS) surface, then converting to Normal(IBOR) or Black volatility when possible. It notes that some emerging-market currencies may still conventionally use Black quotes. The guidance is market- and currency-dependent, rather than a universal rule, and gives no detailed bootstrapping procedure or comparison of numerical results. It therefore helps identify conventions and model limitations, but a practitioner still needs to confirm the relevant market quoting and curve setup.

Key ideas

• Negative rates and negative strikes can make Black volatility impractical for some cap and floor surfaces.
• Normal (Bachelier) volatility is commonly used for caps and floors in affected markets.
• The response identifies OIS discounting with Normal volatility as a popular market setup.
• Volatility may be converted to another convention when the surface permits it.
• Conventions vary by currency, so the market being priced determines the suitable choice.

Tags

# What is the correct volatility to use for inverting Black76?


# What is the correct volatility to use for inverting Black76?












I'm using VCUB on Bloomberg for ATM cap volatilities and have noticed there are a few "flavors" of volatilities. I would like simply use ATM flat vols to bootstrap forward volatilities from caplets using Black's formula.

In this case, I am assuming that Black Vol (IBOR) would be the correct choice for obtaining data on flat implied volatilities from the cap prices (from which fwd vols can be found).

Would anyone know if this is the right way to go? If not, is one volatility favored over another (ex: Black (OIS) vs. Black (IBOR))?

## Answer by oronimbus (score 1)

https://quant.stackexchange.com/a/63497

This depends on the currency you're looking at really. If you are pricing a cap/floor on for example EUR or CHF, then using Black is not particularly useful. The reason is because you have both negative strikes (e.g. -50bp floor) and negative rates which results in a big hole in the volatility surface. You will notice that up to ~10 years time to expiry that you will not be able to generate any vols using Black76.

The solution to this problem would be using the Normal/Bachelier model. There are many posts available such as this one. Most market makers will quote caps/floors in normal bp vol (or forward premia) terms. For some EM currencies you will see that the convention is quoting in Black terms however (perhaps ZAR or KRW?).

In terms of discounting the market standard is to use OIS discounting and hence Normal(OIS) is most popular. Remember that the swap curves (e.g. 6m€L) are OIS (that is €STR) stripped anyways.

Once you have generated your surface with Normal(OIS) you can still convert back to Normal(IBOR) or Black, if possible.

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