Table 20.6 contains quotes for swaps, caps, floors, and European swaptions on November 3, 2008. The 3-month LIBOR was r4(0,0.25) = 2.8588% while the 6-month LIBOR was r2(0,0.5) = 3.0856%.
(a) Interpolate the swap curve at the quarterly frequency, and obtain the LIBOR curve.
(b) Use the Black formula to compute the dollar value of 1 - and 2-year caps (recall that the strike rate equals the swap rate).
Table 20.6

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Maturity Swap Rates Swaption Vols 6M Volatilities 3M 1Y Caps Floors 1 Y 2 Y 2.412/452 678 606 49.3 60.59/61.59 60.59/61.59 2.619/633 9.7 528 1.6 52.26/53.26 52.26/53.26 59. 3.120160 528 46.5 37.7 42.32/43.32 42.32/43.32 353 4 Y 5 Y 7 Y 10 Y 3.507/547 48.7 42.5 35.3 35.99/36.99 35.99/36.99 403 A 21 3.808/822 46.6 34.3 32.24/33.24 32.24/33.24 82 4171/197 413 363 314 27,82/28.82 27.82/28.82 33.1 29.024.21/25.21 24.21/25.21