What Can Go Wrong During Caplet Stripping?

You may or may not have heard that a piecewise-linear interpolation of caplet vols is not stable, it leads to oscillations in the caplet stripping procedure (implying caplet volatilities from cap vol market quotes). And many revert to piecewise-constant interpolation as a consequence. Several years ago, such a case was brought upon myself and I thought at the time that maybe if we used knots at mid-points it would be more stable as it would balance out the weights in the matrix representation, similarly to what is shown in the book A Practical Guide To Splines , which I particularly enjoyed. I also believed that we must be able to do better than piecewise-constant, which has discontinuities in time, and could thus be problematic for any Theta related measure (sensitivity to time).