Modeling the Interest Rate Term Structure: Derivatives Contracts Dynamics and Evaluation

This article deals with a model for the term structure of interest rates and the valuation of derivative contracts directly dependent on it. The work is of a theoretical nature and deals, exclusively, with continuous time models, making ample use of stochastic calculus results and presents original contributions that we consider relevant to the development of the fixed income market modeling. We develop a new multifactorial model of the term structure of interest rates. The model is based on the decomposition of the yield curve into the factors level, slope, curvature, and the treatment of their collective dynamics. We show that this model may be applied to serve various objectives: analysis of bond price dynamics, valuation of derivative contracts and also market risk management and formulation of operational strategies which is presented in another article.