题目
The eighteen-month forward curve is upward sloping with the following sequence of six-month forward rates: F(0,0.5) = S(0.5) = 1.0%, F(0.5, 1.0) = 3.0%, F(1.0,1.5) = 5.0%. What is the price of a $100 face value bond that matures in 1.5 years with a semi-annual coupon that pays a coupon rate of 6.0%?
选项
A.$99.02
B.$100.56
C.$103.89
D.$104.43
答案
D
解析
PV (1st coupon) = $3.0/(1＋1%/2) = $2.99PV (2nd coupon) = $3.0/[(1＋1%/2)×(1 3%/2)] = $2.94PV (final cash flow) = $103/[(1＋1%/2)×(1＋3%/2)×(1＋5%/2] = $98.51.Sum of cash flows = $104.43 (exactly) or 104.44 第一笔票息的现金流折现值：PV (1st coupon) = $3.0/(1＋1%/2) = $2.99 第二笔票息的现金流折现值：PV (2nd coupon) = $3.0/[(1＋1%/2)×(1＋3%/2)] = $2.94 最后一笔现金流折现值：PV (final cash flow) = $103/[(1＋1%/2)×(1＋3%/2)×(1＋5%/2] = $98.51. 总现金流：Sum of cash flows = $104.43 (exactly) or 104.44