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test_3_2009_solutions

test_3_2009_solutions - 1 1.1 test 3 2009 Problem 1 coupon...

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1 test 3 2009 1.1 Problem 1 First find the coupon coupon = ( . 10)(1500) = 150 Then the price is simply 150 1 . 02 + 150 1 . 035 2 + 150 1 . 05 2 + 1650 1 . 07 4 The forward rate (1 + f 3 ) = 1 . 05 3 1 . 035 2 = 1 . 080655 1.2 Problem 2 r = . 05 δ = . 04 S 0 = 45 C ( K, T ) = C (50 , 2) = 4 . 50 P ( K, T ) = P (50 , 2) =??? The put-call premium formula C - P + Ke - rt = S 0 e - δt 4 . 50 - P + 50 e - . 05 * 2 = 45 e - . 04 * 2 P = 8 . 202 1.3 Problem 3 F 0 , 2 =? S 0 = 80 r = . 05 δ = . 07 F 0 , 2 = S 0 e ( r - δ ) t ) = 80 e ( . 05 - . 07)2
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1.4 Problem 4 Define the present values of the bonds purchased a = the present value of 5 year bonds purchased b = the present value of 10 year bonds purchased Match present values a + b = 2000(1 . 08) - 7 = 1166 . 98 Match durations 5 a + 10 b a + b = 7 5 a + 10 b = 7 a + 7 b a = 3 2 b Plugging in from the matched present values
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