Normal Volatility Uses the Bachelier Model for Interest Rate Caps and Floors

Summary

The document addresses a Bloomberg settings question about valuing interest-rate caps and floors when the model is labeled Black-Scholes-Merton and volatility is set to Normal. The response says those choices are not combined: Bloomberg changes the settings to a consistent pair, either Black-Scholes with lognormal volatility or a Normal model with normal volatility. The response identifies the latter as the Bachelier model.

This gives a practical platform behavior and clarifies that normal volatility should not be interpreted as an input that Bloomberg simply converts into lognormal volatility while retaining Black-Scholes. The suggested check is to select the mismatched settings and observe the platform’s automatic change. The note does not explain Bachelier pricing mechanics, instrument conventions, or how Bloomberg handles different product configurations, so the stated behavior is limited to the described interface interaction.

Key ideas

• The response says Bloomberg does not retain a Black-Scholes-Merton model selection with Normal volatility.
• It describes Bloomberg switching to a consistent model and volatility convention.
• The two stated combinations are Black-Scholes with lognormal volatility and Normal with normal volatility.
• The Normal model referenced for caps and floors is the Bachelier model.

Tags

# How does Bloomberg calculate Interest Rate Caps/Floors with Black Scholes Merton Model and Volatility set as "Normal"?


# How does Bloomberg calculate Interest Rate Caps/Floors with Black Scholes Merton Model and Volatility set as "Normal"?












While valuing Interest Rate Caps/Floors in Bloomberg, I saw that we have an option for selecting both Model and Volatility. So, my question is how exactly does Bloomberg value the cap/floor, when we use model as "Black Scholes Merton" and Volatility as "Normal". Is it that Bloomberg converts Normal vol to Lognormal vol (which might differ slightly from the listed Lognormal vols) and values it or do they use any extension/modified version of the Black Scholes model?

## Answer by Hasek (score 1)

https://quant.stackexchange.com/a/74914

> So, my question is how exactly does Bloomberg value the cap/floor, when we use model as "Black Scholes Merton" and Volatility as "Normal".

Well, it doesn't. It will switch both fields either to Black-Scholes and Lognormal or to Normal and Normal. Just try it. Once you try to mix Normal with Black-Scholes and press Enter it will change it to one of the variants above. This answer already answered your question, what you are looking for is called Bachelier model.

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