Curve fitting with Hyman monotonicity preserved
In finance, a common problem is how to create sufficiently smooth curves for pricing, hedging and risk management. This is typically a problem when creating exact fit to interest rate curves.
From the exact fit you often want smooth forward curves of different kinds. Having an extensive collection of interpolators certainly help.
Below is an example of arbitary points and various interpolations. Most interpolations come from the Hermite polynome family, but also cubic spline is there for reference. Clearly when two points are close but on different levels the choice of model will affect the results.
A neat trick found in the latest version of Quantlab 3.1 is to apply a Hyman monotonicity and sign reversal filter to any of the interpolators used. The Hyman filter preserves the exact fit at the expense of the smoothness in the the bends. But it is still not a linear function ...