Pricing Swaptions from Normal and Lognormal Volatility Quotes
Summary
The question concerns calibrating a swaption model when Bloomberg provides normal volatilities at several strikes around the at-the-money forward swap rate. A least-squares calibration requires market prices as targets, but the author does not know which option formula should convert the quoted volatilities into those prices. The response identifies the usual model pairing: normal volatility with the Bachelier formula, and lognormal volatility with the Black formula.
It also points to Bloomberg’s volatility-cube and swaption-pricing functions as tools that apply selected market settings. The answer recommends using the vendor’s implementation rather than building a pricer without understanding those conventions. It does not work through the calibration, specify quote units or settlement details, or discuss when market conventions call for other pricing choices, so the formula pairing is a starting point rather than a complete calibration recipe.
Key ideas
- Normal volatility is associated with the Bachelier model, while lognormal volatility is associated with the Black model.
- A calibration based on volatility quotes needs market prices computed under a consistent pricing convention.
- Bloomberg volatility-cube and pricing functions incorporate settings that affect quoted volatility and swaption prices.
- The response does not provide a worked calibration or detail instrument-specific conventions.
Tags
Full text
# question about the market quote from bloomberg
# question about the market quote from bloomberg
I am a little bit new in finance. Perhaps it is not suitable to ask here, but still, I would like someone can help me.
What I have now in hand are normal volatilities taken from Bloomberg for a swaption 1YX10Y. There are 7 swaption available: USD Swaption Spread 100, USD Swaption Spread 50, USD Swaption Spread 25, USD Swaption ATM, USD Swaption Spread -25, USD Swaption Spread 100, The The description for the with different strikes: ranging from -100bp,-50bp,-25bp,ATM,25bp,50bp,100bp. Suppose the values are 89, 90 ,91, 92, 93, 94, 95 respectively and the current forward swap rate is 5%. How to do the calibration? In general, I should find the least square error of `sum_{i}(Market_Price_{i}-Modeled_Price_{i})^2`. However, when I have a particular model, what I calculate is the modeled price. However, how to calculate the market price? From my realization, I only have normal volatility only, I need to know the standard option formula agreed in market to obtain the market swaption value. What is the option formula then? Follow Black formula or Bachelier formula? Otherwise, I cannot do calibration.
The second question is about the difference between lognormal vol and normal vol. From bloomberg, it states that normal vol measure the absolute movement which lognormal vol measure % movement. Originally, I think lognormal vol should be applied to Black formula while normal vol is applied to Bachelier formula. However, it seems it is not true. Could someone elaborate the ideas a little bit?
## Answer by AKdemy (score 2)
https://quant.stackexchange.com/a/63582
Generally, especially if you are (were) new to finance, you don't want to compute this yourself. BBG has `VCUB` which creates a vol cube based on the market quotes and the selected settings. The help page has a very detailed white paper explaining the implementation.
These vols in turn are used in `SWPM` to price swaptions (and whatever else requires vol). I think it's best to use this pricer as opposed to try to do it yourself.
Normal vol is Bachelier (normal model) Black vol (lognormal) is, as the name implies, Black modelShown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.