中国超长期无套利国债收益率曲线的构建研究

How to Build an Ultra-long Government Bond Yield Curve in China

在债券市场中,收益率曲线的编制处于关键地位,波动性大、编制期限短的收益率曲线不利于各行业尤其是保险业的现金流折现和负债估值。在"偿二代"的监管体系下,中国银保监会对于基础利率曲线的编制要求更高,但由于我国超长期债券市场不够完善,因此收益率曲线的超长端只能通过假设延展形成,这就造成了保险公司准备金的估值对于收益率曲线超长端的假设延展极其敏感。本研究基于终极远期利率的假设,利用B-样条插值和惩罚项平滑的方法拟合收益率曲线,并将远期收益率曲线延展至100年的超长期限,所得曲线拟合效果优良且平稳。通过与其他主流曲线对比分析,本文提出的曲线形态更加平滑,更加符合经济学理论,且在估值案例中的稳定性更优。

Current Chinese mainstream yield curves seem overly fluctuated over the ultra-long end and may not be ideal for discounting cash flows of long-term liabilities,especially for the life insurance companies which have extremely long-term liabilities.With the introduction of China Risk Oriented Solvency System(C-ROSS),the regulator,Banking and Insurance Regulatory Commission,paid much attention to the yield curves used for evaluating the fair value of the liabilities of life insurance companies.To control the ultra-long end(i.e.40 years plus)of the yield curves used by insurance companies,the regulator suggests a constant terminal rate for the ultra-long end.Yet the valuation of the liabilities of life insurers would be sensitive to the assumed terminal rate.We show in the paper how to build an ultra-long yield curve which is less sensitive to the changes in terminal rate and also more stable than current mainstream yield curves.The paper is organized as below:first,we refit the yield curve and extrapolate it to 100 years with smoothing B-Spline interpolation and penalty function;second,we analyze our yield curve and compare it with other mainstream yield curves;third,we conduct further study to verify the efficiency and stability of our yield curve by applying it to liability valuation.