Abstract

This study constructed a risk free term structure based on the Taiwan government bond market, with maturities of up to 120 years. In Taiwan, only government bonds with maturities of up to 30 years could be observed. Additionally, the short-term interest rate also has had spurious volatility and caused the GARCH volatility models to be difficult to converge in the estimation of long-term volatility levels. This paper suggested a threshold GARCH model to infer the equilibrium volatility term structure. Furthermore, this paper used the Vasicek equilibrium interest rate model to extrapolate the long-term interest rate to the Unconditional Forward Rates (UFR) suggested by Quantitative Impact Study 5 (QIS5). The proposed method avoided the arbitrage determination of parameters in QIS5. The numerical analysis showed that the proposed method produced liability values for long-term annuities that were less than that of QIS5.

Key words: Extrapolation, fair valuation, threshold GARCH, unconditional forward rates, Vasicek model.