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本文针对传统利率期限结构拟合曲线存在过度波动问题,构建定价误差绝对距离和波动曲率双重最优化模型,借助对偶几何程序转换为在线性约束区域内的绝对距离最小化问题,并运用负指数平滑立方L1样条和计算几何逼近算法求解模型参数,通过负指数立方L1样条、NSS模型和B样条进行样本内拟合与样本外预测能力的比较,证实负指数立方L1平滑样条对利率期限结构波动的定价精确度、结构性拟合和样本外预测能力均有明显的优势,丰富了国债市场利率期限结构波动与定价的理论基础和研究方法。
Aiming at the problem of excessively fluctuating the fitting curve of the traditional interest rate term structure, this paper constructs a dual optimization model of absolute pricing error distance and fluctuating curvature, and transforms it into the problem of minimizing the absolute distance in the linear constrained area by using the dual geometry procedure. Cubic L1 spline and computational geometry approximation algorithm were used to solve the model parameters. The comparison of in-sample fitting and out-of-sample prediction ability by negative exponential cubic L1 spline, NSS model and B-spline, The pricing accuracy, structural fit and off-sample forecasting ability of term structure volatility all have obvious advantages, enriching the theoretical basis and research methods of the volatility and pricing of interest rate term structure in the bond market.