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# rate_swap - Interest Rate Swaps Introduction Consider the...

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Interest Rate Swaps Introduction Consider the following term structure of interest rates Years to Maturity 1 2 3 Yield Rate 4.5% 5% 6% The implied (forward) annual rates are (check it!) Year 1 Year 2 Year 3 4.500000% 5.502392% 8.028662% We want to find a fixed annual rate R % for all three years that will be equivalent to the implied annual rates above. We first turn the annual rates to money amounts by considering interest earned on \$100 for each year (paid at the end of each year): Year 1 Year 2 Year 3 Interest by Implied Rate 4.500000 5.502392 8.028662 Interest by Fixed Rate R R R 0 1 2 3 4.500... 5.502... 8.028... R R R The two cash-flows should have the same present values at t = 0 (by the term structure), so 4 . 500000 1 . 045 + 5 . 502392 1 . 05 2 + 8 . 028662 1 . 06 3 = R 1 . 045 + R 1 . 05 2 + R 1 . 06 3 (solving) = R = 5 . 932146. Therefore, the fixed rate is 5.932146%. This is the swap rate . Exercise With the same term structure as above, you want to enter an interest rate swap such that the rate for the first year is 0%, and the rates for the second and the third year are both Y %. Find Y .

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