A functional approach to forward rate modelling

Abstract

The aim of this thesis is twofold. First we introduce a Hilbert-valued multi-market two-factor forward curve model satisfying the Heath-Jarrow-Morton equation. Each forward curve consist of a shared source of noise and a specific one, where the noise sources are described by linear affine stochastic differential equations with Q-Wiener noise. Also, we give some insight into the no-arbitrage condition in terms of the covariance operator in the so-called Filipovic space. Secondly, we introduce a branch of statistics called Functional Data Analysis, and perform an empirical study of the historical Norwegian yield curves as Nelson-Siegel smoothed government bond observations in a functional data analysis setting. In particular, we carry out a functional test of stationarity on the norwegian yield curves.