# Attributing the change in NII to Shift, Twist and Butterfly

The movement of the zero rate curves can be decomposed into a shift movement (the level of interest rates) and a twist movement (the slope of the curve) and butterfly (the curvature of the curve). If we want to stress the net interest income (NII) of a bank by shocking these three factors, how do we attribute the change in NII of each of these factors? So far, I have identified following steps. Please correct me if I am going wrong or missing something somewhere:

1. Find the Shift, Twist and Butterfly (STB) - Which one is industry practice to arrive at the shift, twist and butterfly factors from the current term structure- PCA or factor model?
2. Shock S,T,B - Apply the required shock to the Eigen vectors of the three factors
3. Find the new yield curve - Add the new Eigen vectors weighted by their Eigen values to arrive at the new yield curve.
4. Recalculate NII based on the new yield curve - The thing that is not clear to me is how do I attribute the change in NII to the shocks given to shift, twist and butterfly.