求解释

问题如下：

A six-month bond that pays coupons at the rate of 5% per year is currently worth 100.5. The discount factor is 100.5/(100 + 2.5) = 0.980488.

A one-year bond that pays coupons every six months at the rate of 3% per year is currently worth 98.5. What is the one-year discount factor?

解释：

The value of the coupon that will be paid in six months is 1.5 × 0.980488 = 1.4707.

This means that the value of 101.5 received in one year is 98.5 − 1.4707= 97.0293 so that the one-year discount factor is 97.0293/101.5 = 0.955953.

题目问：已知6个月的discount factor为 0.980488。有一个1年债券，couponrate是3%，每半年付息一次，现在价值98.5，求1年的discount factor？

债券价格是未来现金流的折现，所以

98.5 = 1.5×6个月的discount factor + 101.5×一年的discount factor

已知6个月的discount factor=0.980488，

则一年的 discount factor = (98.5 - 1.5×0.980488)/101.5=0.955953.