test_3_2009_solutions

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

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Unformatted text preview: 1 1.1 test 3 2009 Problem 1 coupon = (.10)(1500) = 150 First find the coupon Then the price is simply 150 150 150 1650 + + + 2 2 1.02 1.035 1.05 1.074 The forward rate (1 + f3 ) = 1.053 = 1.080655 1.0352 1.2 Problem 2 r = .05 = .04 S0 = 45 C(K, T ) = C(50, 2) = 4.50 P (K, T ) = P (50, 2) =??? The put-call premium formula C - P + Ke-rt = S0 e-t 4.50 - P + 50e-.052 = 45e-.042 P = 8.202 1.3 Problem 3 F0,2 =? S0 = 80 r = .05 = .07 F0,2 = S0 e(r-)t) = 80e(.05-.07)2 1.4 Problem 4 a = the present value of 5 year bonds purchased b = the present value of 10 year bonds purchased Define the present values of the bonds purchased Match present values a + b = 2000(1.08)-7 = 1166.98 Match durations 5a + 10b =7 a+b 5a + 10b = 7a + 7b 3 a= b 2 Plugging in from the matched present values a = 700.19 b = 466.79 Checking the convexity 52 a + 102 b = 55 a+b Convexity of liabilities = 49 55 > 49 Convexity of assets = 1.5 Problem 5 i = .06 j = 1.062 - 1 = .1236 P V = a.06 + (4)a.1236 tCt v = t=1 t=1 t (1)(t)(1.06) -t + t=1 (2t)(4)(1.1236)-t = (I1,1 a).06 + 8(I1,1 a).1236 1 1 1 1 = + +8 + 2 .06 .06 .1236 .12362 = 882.83 Then the duration = 882.83 PV = 18 ...
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This note was uploaded on 02/28/2012 for the course AMS 318 taught by Professor Timknapik during the Fall '10 term at SUNY Stony Brook.

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

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