Estimation for factor models of the term structure of interest rates: the case of the Taiwanese government bond market

Abstract

This paper examines the O-U process used by Vasicek (1977) and a jump-diffusion process used by Baz and Das ( 1996), for the Taiwanese Government Bond (TGB) term structure of interest rates. We first obtain the TGB term structures by applying the B-spline approximation technique to weekly prices of 45 TGBs from January 6, 1996 to August 29, 1998. We then use the estimated weekly interest rates on the 30-day, 180-day, 5-year, and the IO-year zero-coupon TGBs to estimate parameters for the one-factor and two-factor Vasicek and jump-diffusion models, by using the change of variable technique to obtain the likelihood function in terms of the observed bond prices, and conducting a maximum likelihood estimate. The results show that both the one-factor and two-factor Vasicek and jump- diffusion models are statistically significant, with the two-factor models fitting better. For two-factor models, compared to the second factor, the first factor exhibits characteristics of stronger mean-reversion, higher volatility, and more frequent and significant jumps in the case of the jump-diffusion process. This is because the first factor is more associated with shorter-term interest rates, and the second factor is associated with both short-term and longer-term interest rates. There isn't a great difference in the fitting power of the two-factor Vasicek model and jump-diffusion models, but the jump-diffusion model, which can incorporate jump risks, provides more insight in explaining the term structure as well as the pricing of interest rate derivatives.