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

Abstract

Abstract This paper examines the Ornstein–Uhlenbeck (O–U) process used by Vasicek, J. Financial Econ. 5 (1977) 177, and a jump-diffusion process used by Baz and Das, J. Fixed Income (Jnue, 1996) 78, for the Taiwanese Government Bond (TGB) term structure of interest rates. We first obtain the TGB term structures by applying the B-spline approximation, and then use the estimated interest rates to estimate parameters for the one-factor and two-factor Vasicek and jump-diffusion models. 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 with 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 short-term interest rates, and the second factor is associated with both short-term and long-term interest rates. 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.