I want to bootstrap an (implied volatility) caplet/floorlet surface from quoted cap/floor volatilities 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 (1st picture) seems to be preferable as the linear smiles (2nd picture) are more spiky. 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 go for the linear expiry interpolation. Does anybody have an opinion on that?
How about linear interpolation in variance. As each caplet has a different underlying rate, there is no direct problem with calendar arbitrage. Is linear interpolation in variance nevertheless the better choice than linear interpolation in implied caplet volatility?
Thanks, Bernd
p.s.: 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
