问一道题：NO.PZ2016070201000022

问题如下：

There is a short position in 1-year bonds with a $150 million face value and a 6%annual interest rate, with interest paid semiannually. The annualized interest rate on zero-coupon bonds is 3.8% for a 6-month maturity and 4.1% for a 12-month maturity. Decompose the bond into the cash flows of the two standard instruments, and then determine the present value of the cash flows of the standard instruments. What are the present values of each cash flow?

选项：

解释：

The standard instruments are -150,000,000 x (0.06/2) = -$4,500,000 for six months, and -$4,500,000-150,000,000 = - $154,500,000 for 12 months. The present values are -$4,500,000/1.019 = -$4,416,094, and -$154,500,000 /(1 + 0.041/2)^2 = -$148,355,095.