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Final_F04_Answers

Final_F04_Answers - JOHNSON GRADUATE SCHOOL OF MANAGEMENT...

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JOHNSON GRADUATE SCHOOL OF MANAGEMENT Cornell University NBA–555: Fixed Income Securities and Interest Rate Options Professor Robert Jarrow Tuesday, December 14, 2004 IN CLASS Final Examination Closed Book—One Page of Notes NAME: Answers Note: To get credit, you must show your calculations using the relevant equations.
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3/4 1/4 1/8 7/8 P(0,3) P(0,2) P(0,1) P(0,0) .91514 .94260 .97087 1 = P(1,3;u) P(1,2;u) P(1,1;u) .95513 .97767 1 = P(1,3;d) P(1,2;d) P(1,1;d) .93006 .96408 1 = P(2,3;uu) P(2,2;uu) .98379 1 = P(2,3;ud) P(2,2;ud) .97011 1 = 7/8 1/8 P(2,3;du) P(2,2;du) .97147 1 = P(2,3;dd) P(2,2;dd) .95796 1 = 1 1 1 1 time 0 1 2 3 Figure 1: Evolution of the Zero-Coupon Price Curve The actual probabilities are given on each branch of the tree.
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QUESTIONS For all the subsequent questions, the necessary data is given Figure 1. To get credit, you must show how you compute your answers. (5 points) 1. What are the spot rates? r(0) = 1/.97087 = 1.03 r(1;u) = 1/.97767 = 1.02284 r(1;d) = 1/.96408 = 1.03726 (5 points) 2. What are the money market account values? B(0) = 1 B(1) = 1.03 B(2;u) = 1.03*1.02284 = 1.05352 B(2;d) = 1.03*1.03726 = 1.06837 (5 points) 3. Show that this tree is arbitrage-free by computing the pseudo- probabilities at each node of the tree.
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