题目
The price of a three-year zero coupon government bond is $94.23 and the price of a similar five-year bond is $82.99. Under annual compounding, what is the two-year implied forward rate from year three to year five, F(3,5)?
选项
A.3.67%
B.4.55%
C.5.83%
D.6.56%
答案
D
解析
Note that prices are a function of spot rates: P(3) = F/[1＋s(3)]^3 and P(5) = F/[1＋s(5)]^5no-arbitrage expectation is : [1＋s(3)]^3 × [1 ＋f(3,5)]^2 = [1＋s(5)]^5, such that[1＋f(3,5)]^2 = [1＋s(5)]^5 / [1＋s(3)]^3, and taking square root of both sides:1 f(3,5) = SQRT([1＋s(5)]^5 / [1＋s(3)]^3), such thatf(3,5) = SQRT([1＋s(5)]^5 / [1＋s(3)]^3) - 1, and substituting price in:f(3,5) = SQRT[P(3)/P(5)] - 1.In this case,f(3,5) = SQRT[94.23/82.99] - 1 = 6.56% 请注意，价格是即期汇率的函数：P(3) = F/[1＋s(3)]^3 and P(5) = F/[1＋s(5)]^5 无套利预期是：[1＋s(3)]^3 × [1＋f(3,5)]^2 = [1＋s(5)]^5，则[1＋f(3,5)]^2 = [1＋s(5)]^5 / [1＋s(3)]^3，那么[1＋f(3,5)]^2 = [1＋s(5)]^5 / [1 ＋s(3)]^3 两边开平方1 f(3,5) = SQRT([1＋s(5)]^5 / [1＋s(3)]^3)并将价格替换为f(3,5) = SQRT[P(3)/P(5)] – 1此题中，f(3,5) = SQRT[94.23/82.99] － 1 = 6.56%