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I have DV01 and Gamma Ladder for IR Swaptions and the historical market data of the underlying swap curve. Can someone please help me understand how to calculate historical PNL using taylor expansion for large move in swap curve

Delta: 100k

Gamma Ladder:

Gamma Ladder

If the swap curve changed by 60bp, I believe the delta PNL would be 100k*60. I need help in understanding how the 2nd term of taylor expansion i.e. 0.5 * Gamma * (change)^2 works when we have gamma ladder rather than a single gamma number.

Thanks a lot

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By definition, a Taylor expansion is a local approximation, so you shouldn't use using it for large moves. Also you always have for options a 'gamma ladder', as gamma is a function of the underlying. One thing you could try maybe is to fit a curve to you gamma profile, then use a numerical method to calculate the derivative at your current point. This will give you Speed (the derivative of gamma with respect to the underlying, so your swap rate). Then you plug in that Speed number into your Taylor expansion up to the 3rd order.

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