I'd like to quantify the difference between 2 Foward Curves. In particular, I'd like to get a single metric which represents the magnitude of change between curve A and curve B. I'd like to plot this in time to see how this "magnitude" changes with time. I understand this metric will lose a lot of information about each curve but ideally it is larger for curves that are more different than for curves that are less different.
There are many techniques one can use to compare curves from geometry and signal processing which can deal with scaling, rotation etc. Forward curves are rather simple constructs and I wonder if there exist simple methods that can be used to do this? Before I write some code to do this, I was wondering if there is a standard method to do this?
For example, a simple metric might be the mean sum of squares of the differences between the curve points. Unfortunately, this does not take into account curves that are exactly the same slope-wise but are shifted up/down and when it comes to Forward Curves, slope is more important than absolute position.