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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?

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