随着中国利率市场化进程的推进和利率衍生产品的丰富,利率作为证券定价的核心变量之一,如何对其进行有效预测成为资产定价的关键。无套利DNS利率模型是在DNS模型的基础上发展而来,理论研究表明它是受约束的高斯仿射过程。本文以2005-2012年上交所国债价格月度数据隐含的利率期限结构为样本,利用准极大似然法对无套利DNS模型和DNS模型进行估计,研究结果表明:无套利DNS模型兼顾了仿射利率模型的无套利条件和DNS模型实证效果;它保持了DNS模型的预测优势,所有期限的预测误差都在1.5个基点以内;模型常数调整项的特征是随着利率期限的延长,调整力度逐步增强。
With the deep development of Chinese interest rate marketization and the diversification of the interest rate derivatives,how to predict interest rate effectively,as one of the kernel variables in securities pricing, has become a key work. The no-arbitrage DNS model is developed on the basis of DNS model, and theoretical studies show that it is a constrained affine Gauss process. With the term structure of yields implied in monthly bonds price from 2005 to 2012 in Shanghai Stock Exchange (SSE), the no-arbitrage DNS model and the DNS model are studied empirically using the method of quasi-maximum likelihood. Are the results show that the no-arbitrage DNS model keeps the no arbitrage condition of affine term structure model and good empirical results of DNS model; and also it keeps the forecast advantage of DNS model, because prediction errors of all term structures in both two models are within 1.5 basis points; and also the characteristics of constant adjustment item show that the value is increasing with the extension of maturities.
[1] Diebold F X, Li Canlin. Forecasting the term structure of government bond yields[J]. Journal of Econometrics, 2006, 130(2):337-364.
[2] Nelson C R, Siegel A F. Parsimonious modeling of yield curves[J]. Journal of Business, 1987,60(4):473-489.
[3] Vasicek O. An equilibrium characterization of the term structure[J]. Journal of Financial Economics, 1977, 5(2):177-188.
[4] Cox J C, Ingersoll Jr J E, Ross S A. A theory of the term structure of interest rates[J]. Econometrica, 1985, 53(2):385-407.
[5] Longstaff F A, Schwartz E S. Interest rate volatility and the term structure: A two-factor general equilibrium model[J]. Journal of Finance, 1992, 47(4):1259-1282.
[6] Duffie D, Kan R. A yield-factor model of interest rates[J]. Mathematical Finance, 1996, 6(4):379-406.
[7] Duffee G R. Term premia and interest rate forecasts in affine models[J]. Journal of Finance, 2002, 57(1):405-443.
[8] Dai Qiang, Singleton K J. Expectations puzzles, time-varying risk premia and affine models of the term structure[J]. Journal of Financial Economics, 2002, 63(3):415-441.
[9] Kim D, Orphanides A. Term structure estimation with survey data on interest rate forecasts[J]. Journd of Financeal and Quantitative Analysis,2012,47(1):241-272.
[10] Filipovic D. A note on the Nelson-Siegel family[J]. Mathematical Finance, 1999, 9(4):349-359.
[11] Diebold F X, Piazzesi M, Rudebusch G D. Modeling bond yields in finance and macroeconomics [J]. American Economic Review, 2005, 95(2):415-420.
[12] Jacobs K, Li Xiaofei. Modeling the dynamics of credit spreads with stochastic volatility[J]. Management Science, 2008, 54(6):1176-1188.
[13] Christoffersen P, Dorion C, Jacobs K. Nonlinear kalman filtering in affine term structure models[J].Management Science,2014,60(9):2248-2268.
[14] 周子康,王宁,杨衡. 中国国债利率期限结构模型研究与实证分析[J]. 金融研究,2008,(333):131-150.
[15] 吴恒煜,陈鹏,严武,等. 基于Copula的两因子Vasicek利率模型实证研究[J]. 管理学报,2010,7(10):1529-1534.
[16] 周荣喜,王晓光. 基于多因子仿射利率期限结构模型的国债定价[J]. 中国管理科学,2011,19(4):26-30.
[17] 文兴易,黎实. 基于局部线性逼近的利率期限结构动态NS模型[J].管理学报,2012,9(7):975-978.
