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

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