题目
If the spot rate term structure is flat, what is true of the discount function (i.e., the set of discount factors) as function of maturity?
选项
A.Flat
B.Increasing with maturity
C.Decreasing with maturity
D.Insufficient information: we need the yield (YTM) to answer
答案
C
解析
Greater maturity requires more discounting. For example if the spot rate term structure is flat at 5%, then semi-annual discount function is: d(0.5) = 0.9756, d(1.0) = 0.9518, d(1.5) = 0.9286 ...In regard to (D), please note that a flat spot/zero term structure is the special case where the yield must match; e.g., flat spot rates at 5% imply yield must also be 5%. 到期日更长则折扣率越高。若即期汇率的期限结构一直是5%，则半年的折扣函数为：d(0.5) = 0.9756, d(1.0) = 0.9518, d(1.5) = 0.9286 ... 对于选项D，请注意一个现货/零期限结构是收益必须匹配的特殊情况； 例如，5％的固定现货利率意味着收益率也必须为5％。