Building Curves Using Area Preserving Quadratic Splines

Abstract

We compare two interpolation methods which are widely used to construct discount curves, forecast (projection) curves, basis curves, and other financial curves. We find that the area-preserving, quadratic-spline method is superior to the “smart quadratic” method, yielding smoother, more natural looking forward curves with few of the artifacts exhibited by the smart quadratic curves. We also show how to efficiently implement both methods by an iterative bootstrapping scheme.