Abstract: Based on the minimization principle of quadratic sum on pricing error for term structure of interest rate (TSIR), we introduce a geometric transformation program to solve optimization of absolute value on pricing error with nonlinear constraints, which enriches theory framework and research methods on pricing and volatility of interest rate in T-bill Market. To overcome excessive sensitivity of B-spline's node distribution and C² smoothness condition of discount function, we introduce negative exponential smoothness cubic L₁-spline optimization model with optimal constraint of absolute value of estimate error and second derivative of discount function, to increase the estimate, pricing and prediction ability of short-term interest rate's volatility structure mutation, improve the advantage on depicting the medium or long term interest rate volatility trend, and reduce the excessive volatility of TSIR estimate based on NSS model and B-spline.

Key words: t-bill market, term structure of interest rate, geometric transformation program, volatility

摘要： 本文变革已有的利率期限结构模型估计依赖于定价误差平方和最小化原则,引入几何双重变换程序解决非线性约束的误差绝对距离最小化问题,丰富国债市场利率波动和定价研究的理论体系和研究方法;运用负指数平滑立方L₁样条优化模型,克服B样条函数对节点数目与定位的过度敏感和放宽对贴现函数的二阶导数平滑要求,协同拟合误差绝对距离与贴现函数波动率最小化,保留B样条函数刻画中长期利率波动趋势的优势,增强对短期利率波动结构突变的估计、定价和预测能力,缓解B样条和NSS模型在利率期限结构拟合存在的过度波动问题。

关键词: 国债市场, 利率期限结构, 几何变换程序, 波动