问一道题：NO.PZ201903040100000101

问题如下：

1.Based on Exhibit 1, Johnson should price the three-year Libor-based interest rate swap at a fixed rate closest to:

选项：

0.34%.

1.16%.

1.19%.

解释：

C is correct. The swap pricing equation is

$ϒ_{FIX}=\frac{1-PV_{0,t_n}(1)}{\displaystyle\sum_{i=1}^n{PV_{0,ti}(1)}}$

That is, the fixed swap rate is equal to 1 minus the final present value factor (in this case, Year 3) divided by the sum of the present values (in this case, the sum of Years 1, 2, and 3). The sum of present values for Years 1, 2, and 3 is calculated as

$\sum_{i=1}^nPV_{0,ti}{(1)}\text{ }=\text{ }0.990099\text{ }+\text{ }0.977876\text{ }+\text{ }0.965136\text{ }=\text{ }2.933111$

Thus, the fixed-swap rate is calculated as

^{$<\mathrm{/}sup><\mathrm{/}em><i>{\gamma }_{FLX}=\frac{1-0.965136}{2.933111}=0.01189or1.19\mathrm{\%}$}\gamma_{FLX}=\frac{1\text{ }-\text{ }0.965136}{2.933111}=0.01189\text{ }or\text{ }1.19\%</sup></em><i>γFLX​=2.9331111 − 0.965136​=0.01189 or 1.19%