Libor Market Models Within the Affine and Quadratic Models

Abstract

We are going to use the properties of the Affine and Quadratic jump-diffusion models to formulate a general theory of the libor market model that is consistent with the pricing of both caplets and swaptions. We will assume certain types of processes for the dynamic of the forward rates and their instantaneous volatilities with well known analytic characteristic functions in order to get closed-form solutions for the pricing of caplets and semi-closed-form solutions for swaptions in a stable and efficient manner.

Keywords: libor market model , Affine and Quadratic jump-diffusion models, smile