Quantifying the interest rate risk of bonds by simulation

Abstract

Managing interest rate risk of bonds is very important in practice. Therefore, many methods have been developed to measure the interest rate risk. In this thesis, simulation is used to quantify the interest rate risk of bonds. Only government bonds are considered, which are often assumed to have “0” default risk. So, the only relevant risk is the interest rate risk. In this thesis popular interest rate models are analyzed in a practical framework. Bond pricing, interest rate simulation, parameter estimation and risk simulation principles are explained for six different short-rate models. For each model, the exact method for simulating the short-rate is given; the analytical bond prices of the models and the bond prices obtained by simulation are compared; MLE is used to estimate the model parameters and risk simulations are made including a sensitivity analysis of VaR with respect to the model parameters. In the last part of this thesis, the risk estimation performance of the different models is compared. The US, German and the Canadian bond market data are used for analysis. The quality of the risk estimates of the models for different maturities is assessed. It is observed that for all models and data that the arbitrage-free and the equilibrium versions lead to the same Value at Risk results. For all implementations we use R, which is a programming language for statistical computing.