Interest rate modelling and bond portfolio selection

Abstract

Bond portfolio management and interest rate risk quanti cation is an important eld of practice in nance. In markets there exist di erent types of bonds that are issued from a variety of sources including the central banks, municipalities, and corporations. In this thesis only government bonds, i.e. zero-coupon bonds that are assumed to be non-defaultable are considered. Bond dynamics can be analyzed with the help of interest rate models. In this thesis two popular interest rate models, Vasicek Model and LIBOR Market Model, are analyzed in a practical framework for the nal aim of using for bond portfolio management problem. For each model stochastic dynamics, parameter estimation, bond pricing, and interest rate simulation are introduced. In the last part of this thesis Markowitz's Modern Portfolio Theory is introduced and it is shown how it is adapted for bond portfolio selection problem. The traditional mean / variance problem and its modi ed version, mean / VaR problem, are solved for both model. Term structure models are used to estimate expected returns, return variances, covariances and value-at-risk of bonds with di erent maturities. For all implementations R, which is a programming language for statistical computing is used.