Pricing Interest Rate Derivatives Under Different Interest Rate Modeling: A Critical and Empirical Comparison

Abstract

This paper deals with issues related to the choice of the interest rate model to price interest rate derivatives. After the development of the market models, choosing the interest rate model has become almost a trivial task. However, their use is not always possible, so that the problem of choosing the right methodology still remains.

The aim of this paper is to compare some of the most used interest rate derivatives pricing models to understand what are the issues and the drawbacks connected to each one. It is shown why and in which cases the use of each model does not give appreciable results and when, on the other hand, the opposite occurs. More exactly, it will be shown that the lack of data on the implied volatilities or the inefficiencies in the financial market can prevent the use of the market models, because a satisfying calibration of the interest rate trajectories cannot be guaranteed. Moreover, it is shown how the smile effect in the interest rate options market can affect the price provided by each model and, more exactly, that the difference between the price provided by the models and the observed market prices gets larger, as the strike price increases.

Keywords: Cox Ingersoll and Ross, Black Derman and Toy, Libor Market Model, Lognormal Forward-Libor Model, cap, interest rate risk

JEL Classification: G12, C53, C65