Implementation of the Heath-Jarrow-Morton model on the Turkish Government zero-coupon bonds

Abstract

The term structure of interest rates explains the relationship among interest rates on default-free securities that vary in their time to maturity. The evolution of the term structure of interest rates through time reflects the future expectations of the market. There is a wide range of approaches including the equilibrium models and arbitrage-free models, all of which try to describe the term structure of interest rates and price interest rate sensitive financial instruments. This thesis focuses on a specific arbitrage-free model called Heath-Jarrow-Morton (HJM), and tries to structure the term structure based on the forward rates. The forward rates are obtained from the prices of zero-coupon bonds issued by the Turkish Government. The evolution of forward rates is described by a multi-factor HJM model with pre-specified drift and volatility functions. The parameters of the models are estimated by an historical procedure using a statistical Principal Component Analysis (PCA). The estimated parameters are used in a simulation algorithm to forecast the future zero-coupon bond prices. The computational results show that the model slightly underprices the real zero-coupon bonds. This deviation between the model and real prices are tried to be explained by a multiple linear regression analysis. Some global and domestic economic indicators are used to understand the relations. The performance evaluations indicate the success of the HJM model together with an error forecast based on specific economic parameters.