Homework - JOHNSON GRADUATE SCHOOL OF MANAGEMENT Cornell...

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JOHNSON GRADUATE SCHOOL OF MANAGEMENT Cornell University NBA–555: Fixed Income Securities and Interest Rate Options Professor Robert Jarrow Homework (Not Graded) For Self Study
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QUESTIONS 1. a. Given . ) 0 , 0 ( f ) 1 , 0 ( f ) 2 , 0 ( f ) 3 , 0 ( f compute , 96154 . 92456 . 88053 . 83860 . ) 1 , 0 ( P ) 2 , 0 ( P ) 3 , 0 ( P ) 4 , 0 ( P = b. Using question 1(a), compute the time 0 value of a coupon bond with cash flows: time cash flow $5 $5 $100 01 2 3 4
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2 P(0,4)=.8386 P(1,4;u) = .8886 P(1,4;d) = .8557 r(0) = 1.04 7/ 8 1/ 8 r(1;u) = 1.03277 P(2,4;uu) = .93 P(2,4;ud) = .9055 r(1;d) = 1.04733 P(2,4;du) = .9081 P(2,4;dd) = .8842 5/ 9 4/ 9 1/ 6 5/ 6 Figure: A Four-Period Zero-Coupon Bond Price and Spot Rate Process at Times 0, 1, 2. Actual Probabilities Along the Branches of the Tree
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3 2. Compute the money market account's value, showing your calculation. B(1) = B(2;u) = B(2;d) = 3. Is this tree arbitrage-free? Prove your answer by computing the pseudo-probabilities along each branch of the tree. Show your calculations. Round your answer to the nearest simple fraction (e.g., write .249987 as .25 or 1/4).
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This note was uploaded on 10/31/2010 for the course NBA 5550 at Cornell.

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Homework - JOHNSON GRADUATE SCHOOL OF MANAGEMENT Cornell...

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