Actuarial Outpost > SoA IRM: MIP Example 9-8 on page 621
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#1
08-22-2018, 02:48 PM
 918273 Member SOA AAA Join Date: Jul 2016 Studying for DMAC Posts: 76
IRM: MIP Example 9-8 on page 621

In part 2 of the example, I don't understand why the floating leg would only make one payment at time 2 months, instead of one payment at time two months and another at time 8 months. Why wouldn't the present value of the floating payments (plus hypothetical notional principal) instead be 0.0345(0.9881) + 1.0345(0.9531) = 1.0201? Problem follows:

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Consider a plain vanilla interest rate swap with two months to go before the next payment. Six months after that, the swap will have its final payment. The swap fixed rate is 7 percent, and the upcoming floating payment is 6.9 percent. All payments are based on 30 days in a month and 360 days in a year. Two-month LIBOR is 7.250 percent, and eight-month LIBOR is 7.375 percent. The present value factors for two and eight months can be calculated as follows:

$\dfrac{1}{1+0.0725(60/360)} = 0.9881$
$\dfrac{1}{1+0.07375(240/360)} = 0.9531$

The next floating payment will be 0.069(180/360) = 0.0345. The present value of the floating payments (plus hypothetical notional principal) is 1.0345(0.9881) = 1.0222. Given an annual rate of 7 percent, the fixed payments will be 0.07(180/360) = 0.035. The present value of the fixed payments (plus hypothetical notional principal) is, therefore, 0.035(0.9881) + 1.035(0.9531) = 1.0210.