(An) empirical study of bayesian MCMC method on term structure models

Abstract

The thesis studies on a Bayesian MCMC method in order to implement its advantageous features, such as data augmentation and simulation without optimization, to short term interest rate models for Korean 3 months Treasury bond yield rate. The aim is to estimate parameters particularly from the Vasicek model and its extensional model with a jump component, and to compare them with the resulting outcomes under different conditions. The one factor model due to Vasicek provides an excellent test case for illustrating the ideas developed in MCMC as it is relatively simple yet nonlinear. Mil algorithm successfully finds the target distribution of parameters better than MLE. Discretization bias associated with the Euler scheme used to approximate the continuous time model is reduced by incorporating latent augmented data. The result implies that a jump factor does not explain much of the weekly interest rate by itself even if it shows the lowest error. MCMC method vastly reduces errors and improves accuracy of the estimation, needless to mention its convenient approach to deal with many parameters including missing ones at the same time. In conclusion, MCMC tremendously improves its performance and is expected to be even more powerful with inclusion of other factors such as jumps and stochastic volatility.