Interpolation Methods in Interest Rate Applications

This chapter discusses interpolation, an important tool in many financial applications. It is required that the output of the interpolation satisfies some quality criteria related to the nature of the problem. The chapter addresses these requirements and proposes several interpolation methods that satisfy them. It deals with the problem of preserving the shape of data in the interpolant. The geometric properties are taken into consideration, for example preventing spurious behaviour near points where rapid changes take place. This may be even more important than ensuring the asymptotic accuracy of the interpolation method. Starting from popular interpolation methods such as linear and cubic spline, the chapter also focuses on: the Hyman filter, positivity-preserving rational cubic interpolation, Akima method and Hagan-West approach called Forward Monotone Convex Spline. The chapter completes the interpolation suite with a discussion on bilinear interpolation and a C# framework to explore the impact of using different interpolation schemes.