No.PZ2020021204000034 (问答题)来源: 原版书
A bond that can be delivered in the December 2018 ten-year Treasury note futures contract is a bond with maturity on April 15, 2026, that pays a coupon of 4% per annum.When the yield is 6% per annum(with semi-annual compounding) ， calculate the conversion factor for the bond.
解析
The bond's time to maturity on the first day of the delivery months is seven years (December 2018 to December 2025) and 4.5 months (January 2026 to mid-April 2026).This is rounded to seven years and three months. The dirty price of a seven year and three-month bond immediately before the coupon payable in three months is
∑i=01421.03i+1001.0314=90.7039∑i=0141.03i2+1.0314100=90.7039
when the yield is 6%. The dirty price of the bond three months earlier is
90.70391.03=89.37321.0390.7039=89.3732
Subtracting the accrued interest of 1, we get a clean price of 88.3732 and the conversion factor is 0.8837.
为什么7年零4.5个月可一round成7年3个月？又为什么按照半年复利一次，bond往前折算了14期后，是除以 √1+0.03
