Equivalence between forward rate interpolations and discount factor interpolations for the yield curve construction

TL;DR

This paper demonstrates the equivalence between forward rate and discount factor interpolations in yield curve construction, clarifying their relationships and differences in various interpolation methods.

Contribution

It reveals that popular forward rate interpolation methods are mathematically equivalent to classical discount factor interpolations, clarifying their connections.

Findings

Forward rate and discount factor interpolations can be equivalent.

Clarification of differences between various forward rate interpolations.

Provides insights into yield curve construction methods.

Abstract

The traditional way of building a yield curve is to choose an interpolation on discount factors, implied by the market tradable instruments. Since then, constructions based on specific interpolations of the forward rates have become the trend. We show here that some popular interpolation methods on the forward rates correspond exactly to classical interpolation methods on discount factors. This paper also aims at clarifying the differences between interpolations in terms of discount factors, instantaneous forward rates, discrete forward rates, and constant period forward rates.