test_3_2008_solutions

# test_3_2008_solutions - K 1 and short put with strike K 2...

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1 test 3 2008 1.1 Problem 1 1. I forgot to mention the interest rate is 5%. My apologies for the confusion. Break the two streams of cash into \$100 from t = 1 , ··· , 20 \$100 from t = 11 , ··· , 20 2. Then we write the duration as tC t v t C t v t = 20 t =1 100 tv t + 10 t =1 100( t + 10) v t +10 100 a 20 i + 100 a 10 i v 10 = 100( I 1 , 1 a ) 20 i + v 10 ( 10 t =1 100 tv t + 10 t =1 1000 v t ) 100 a 20 i + 100 a 10 i v 10 = 100( I 1 , 1 a ) 20 i + v 10 (100( I 1 , 1 a ) 10 i + 1000 a 10 i ) 100 a 20 i + 100 a 10 i v 10 = 10 . 6104 3. Now we equate present values 3000(1 . 05) - t = 100 a 20 i + 100 a 10 i v 10 t = - ln ± 100 a 20 i + 100 a 10 i v 10 3000 ² /ln (1 . 05) t = 11 . 40 1.2 Problem 2 1. Coupon = . 06 * 1000 = 60 2. Price = 60(1 . 06) - 1 + 60(1 . 07) - 2 + 1060(1 . 08) - 3 = 950 . 47 3. Ignore the yield rate question 4. (1 + f 3 ) = (1+ s 3 ) 3 (1+ s 2 ) 2 = 1 . 1003 1.3 Problem 3 1. A put option with strike K allows you to sell a single share of stock for K dollars. You would much prefer to have the right to sell the stock for \$200 versus \$100, thus the premium for a 200 strike put option should be higher than a 100 strike put option. 2. One possible solution would be to purchase a long put with strike

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Unformatted text preview: K 1 and short put with strike K 2 where K 1 &gt; K 2 1.4 Problem 4 Dene the present values of the bonds purchased a = the present value of 6 year bonds purchased b = the present value of 9 year bonds purchased Match present values a + b = 100(1 . 07)-7 + 100(1 . 07)-8 = 120 . 48 Match durations 6 a + 9 b a + b = 7 * 100(1 . 07)-7 + 8 * 100(1 . 07)-8 100(1 . 07)-7 + 100(1 . 07)-8 6 a + 9 b a + b = 7 . 483 6 a + 9 b = 7 . 483 a + 7 . 483 b a = 1 . 023 b Plugging in from the matched present values a = 60 . 92 b = 59 . 533 Checking the convexity Convexity of assets = 6 2 a + 9 2 b a + b = 58 . 24 Convexity of liabilities = 7 2 * 100(1 . 07)-7 + 8 2 * 100(1 . 07)-8 100(1 . 07)-7 + 100(1 . 07)-8 = 56 . 24 58 . 24 &gt; 56 . 24...
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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_2008_solutions - K 1 and short put with strike K 2...

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