Curiosities on the Monotone Preserving Cubic Spline

In this paper we describe some new features of the monotone-preserving cubic splines and the Hyman’s monotonicity constraint, that is implemented into various spline interpolation methods to ensure monotonicity. We find that, while the Hyman constraint is in general useful to enforce monotonicity, it can be safely omitted when the monotone-preserving cubic spline is considered. We also find that, when computing sensitivities, consistency requires making some specific assumptions about how to deal with non-differentiable locations, that become relevant for special values of the parameter space.

Keywords: Yield curve, fixed-income, interpolation, Hyman, monotone preserving cubic splines.

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