I want to bootstrap an (implied volatility) caplet surface from quoted caps on a fixed strike grid. I'm thinking about either using a left-continuous or a linear interpolation in expiry dimension. If one just looks at the smiles of each quoted cap expiry left-continuous (2nd picture) seems to be preferrable as the linear smiles (1st picture) are more spicky. However, a left-continuous interpolation will produce theta jumps. The jump always happens for a (standard) cap in the portfolio on the day when it's schedule aligns with schedule of the caps used to bootstrap the surface.
Therefore, out of these 2 candidates, I would clearly go for the linear expiry interpolation. Does anybody have an opinion on that?
ps: I still have to implement a linear interpolation in variance. Is this still considered to be the best method out of the straightforward ones?
pss: I know that there are more fancy interpolation methods out there (e.g. using SABR smiles with interpolation on the SABR parameters) but I want to go for a simple interpolation as a starting point