Forward versus Spot Interest Rate Models of the Term Structure

Abstract

Valuation theory for derivatives based on interest rates and bond prices continues to be in flux. A wide variety of models have been introduced over the years, and many are still actively used. Some are based on modeling the behavior of spot interest rates, with enough structure that the model is constrained to be consistent with the current market term structure. Others begin with the observed term structure and model behavior of the forward rates embedded in it. Moraleda and Pelsser conduct a comparison of five of the most common interest rate models, including some of each type. The data used include U.S. spot interest rates for maturities out to ten years and dollar cap and floor prices. The authors find that the models of the spot rate appear to outperform those based on forward rates, with the Black-Karasinski model doing the best overall.