核心算法 / Core algorithm

 

零息收益率曲线的半参数表

Semi-Parametric Representation of the Zero-Coupon Yield Curve

 

 

To handle the complexities of the Chinese fixed income market, SuperCurve^® has chosen a semi-parametric approach to model the 

zero-coupon curve. The spline representation, the number of splines and the fitting algorithm have been carefully chosen to provide 

consistent and stable prices that permanently reflect the current state of the market.

剩余期限和利率的对数标度

Logarithmic Scale for the Maturity and the Rates

 

 

 

The volatility of interest rates is more or less proportional to the level of the rates when the inflation and the rates are high, but 

independent of their level when the inflation is low and rates are low as well, if not negative, as we often see today. SuperCurve^®

uses shift parameter for second change of variable in the rate level. 

 

脊最小二乘准则和振荡控制

Ridge Least Square Criterion and Oscillations Control

 

 

 

SuperCurve^® minimizes the Least Square Criterion, the first term of the objective function aims at fitting the theoretical price of each 

bond to its real price. The second term is ridge regularization to ensuring the regularity of the yield curve.

 

有效统计和误差消除

Robust Statistics and Error Elimination

 

 

中国固定收益市场的价格和收益率数据往往远离实际市场情况，要么是因为报价长期没有更新，要么是因为这些是虚假的

或预先安排的交易，它们的价格不符合当前的市场情况，这会使得一些价格无法由参数法或者半参数法拟合。SuperCurve^®

用M估计优化最小二乘目标函数，以减少估值偏差的影响；系统将过滤掉价格不匹配的债券，并且用其他债券重新拟合曲线。

 

Price and yield data in the Chinese fixed-income market are often away from the actual market situation, either because quotes have 

not been updated for a long time or because these are fake or pre-arranged trades at prices that are not in line with the current market 

situation. To address this issue, robust techniques are used. First, replacing the simple square in the objective function of Least Square 

Criterion by an M-estimator reduces the influence of poorly fitted prices. Then by filtering out bonds whose price cannot be correctly 

matched and re-running the fitting procedure without these bonds.

 

实时拟合

Real-Time Fitting

 

不同剩余期限的信息输入是无序的，因而需要使用特定技术将其进行组合，以使新的价格及收益率与之前的信息保持一致。

基于贝叶斯统计，每次在收到一个或多个新报价时，我们引入卡尔曼滤波这一自适应的方法能够高效地更新整条零息曲线，

并实时调整系数以匹配新的报价。同时，这也可以有效地解决了数据缺失问题。

 

Information on various parts of the maturity range arrives in a disorganized manner. It needs specific techniques to be combined to 

merge new prices and yields coherently with past information. Based on Bayesian statistics, SuperCurve® adapts Kalman filtering 

method to optimally update the whole zero-coupon curve each time one or several new quotes are received. This can efficiently 

solve the problem of missing data. 

 

拟合IRS曲线

Fitting the IRS Curve

 

 

鉴于利率互换可视作一只具有相同期限的虚拟债券，我们可以按照债券曲线的拟合方式来拟合IRS零息曲线。因为

SuperCurve^®只拟合为数不多的期限对应的利率互换收益率，我们可以调整收益率曲线系数，以确保这些参考互换收益率

与通过定价模型计算的理论值完全匹配。

 

We use this equivalence to calibrate the IRS zero-coupon curves in the same way we calibrate the bond curves. Thanks to the fact 

that we must only fit a small number of swap rates at fixed maturities, we can adjust the yield curve coefficients and ensure that 

these reference swap rates match their theoretical values from the model.

 

非国债曲线的拟合

Fitting Curves Other Than Treasury Bonds

 

 

国债收益率的任何波动都会即时影响到其他类型债券或利率互换的收益率水平，为确保不同收益率曲线的拟合保持一致性，

SuperCurve^®运用了不同品种曲线系数，例如(αcdb，βcdb)和(αTB，βTB)之间的偏移系数，实现拟合国开债、农发和口行债，

以及利率互换（基准利率为SHIBOR3M和FR007）。

 

Any fluctuation on the Treasury Bonds yield would tend to be immediately reflected on the other bond or IRS. SuperCurve^® use the shift in 

coefficients between (αcDb,βcDb) and (αTb,βTb). So it can be applied to CDB, EIBC & ADBC and IRS (both SHIBOR3M and FR007).

 

税收调整

Tax Adjustment

 

 

与其他债券不同，国债息票免税。存在税前和税后收益差。SuperCurve^®在给国债定价时，考虑了免税因素对理论收益率

的影响。

 

Contrary to other bonds, the coupons paid by Treasury Bonds (TB) are not taxable. This induces a price difference between these bonds 

and other taxable bonds, the higher the coupon, the larger the difference. SuperCurve® incorporate the tax-exempt feature into the TB 

fitting curve.