关键词: 动态Nelson-Siegel模型, 无套利约束, 仿射期限结构模型, 中债国债收益率

Abstract: The Dynamic Nelson-Siegel term structure model (DNS) of bond yields, which has good empirical performance, has the theoretical flaws that cannot exclude arbitrage opportunities. However, the No-Arbitrage Affine Term Structure model (NA_ATSM), which compatible with the financial theory with no-arbitrage constraint, does not perform well in the empirical application.
Therefore, the comparison and combination of the two kinds of models are the goals of many literatures. In this paper, the DNS model and the NA_ATSM model are estimated and compared to explore the characteristics of the yield curves in China treasury bond market. Furthermore, the yield curve latent factors generated by the DNS model is used to estimate the NA_ATSM model and further to test whether they were compatible with the no-arbitrage constraint.
The end-of-month yields of China treasury bond market from March 2006 to December 2017 with 142 sample months are used, consisting of 10 maturities of 1, 3, 6, 9, 12, 24, 36, 60, 84 and 120 months from Wind Financial Database which are derived with Hermite interpolation method from three different market segments, such as the interbank market, stock exchange market and over the counter market. The most active market is the interbank bond market, which provides transaction of bonds for commercial banks, securities companies and other institutions.
In the empirical analysis, the DNS model of the term structure is estimated, and then the NA_ATSM model is estimated by using the factors extracted from the DNS model as exogenous factors. It is concluded that there is the time-varying risk price of risk, which confirms the existence of term premia in China Treasury bond market. However, it is also found that there is no significant difference between the two models in fitting performance, and there is no evidence that no-arbitrage constraint can help to improve the forecast performance.
Second, given the assumption of independent normality of the cross-section equations of yields and the assumption of joint normality of state vectors, a number of artificial data of interest rate and state factors generating are reconstructed by Monte Carlo simulation method. Under the estimation and test with the simulated data, it is found that the factor loadings under the no-arbitrage model is statistically different from the loadings from the Dynamic Nelson-Siegel model, which means there is a significant inconsistency between the yield curve generated by the DNS model and the no-arbitrage constraint in the China bond market, that is, there is no evidence to reject the hypothesis of existence of arbitrage opportunities in the China treasury market.

Key words: dynamic Nelson-Siegel model, no-arbitrage restriction, affine term structure model, China treasury yields