SolA6_part1

# SolA6_part1 - SOLUTION FOR ASSIGNMENT 6 PART 1(1 Solution...

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SOLUTION FOR ASSIGNMENT 6 PART 1 (1) Solution 0.1. let r 1 ,r 2 ,r 3 be spot rates for year 1, year 2 and year 3. we have 106 . 7961 = 110 / (1 + r 1 ) 94 . 4588 = 2 / (1 + r 1 ) + 102 / (1 + r 2 ) 2 100 . 7571 = 8 / (1 + r 1 ) + 8 / (1 + r 2 ) 2 + 108 / (1 + r 3 ) 3 solve the equations, one has r 1 = 0 . 03 , r 2 = 0 . 05 , r 3 = 0 . 08 and the price for the three year bond is 12 / (1 + r 1 ) + 12 / (1 + r 2 ) 2 + 112 / (1 + r 3 ) 3 = 111 . 44 (2) Solution 0.2. Since all bonds are zero coupon bonds, so P i = 100 / (1 + r i ) i , i = 1 , 2 , 3 , 4 , 5 where P i are the price for year i bond and r i are the spot rate for the year i. solve the equations we have r 1 = 0 . 03 , r 2 = 0 . 05 , r 3 = 0 . 07 , r 4 = 0 . 08 , r 5 = 0 . 092479 and therefore f [3 , 4] = (1 + r 4 ) 4 / (1 + r 3 ) 3 - 1 = 11 . 0564% (3) Solution 0.3. Without loss of generosity, we can assume the face value is 100. Notice the cash ﬂow is C 1 = C 2 = C 3 = C 4 = 8 , C 5 = 108 and the price of the cash ﬂow is P = 4 X

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SolA6_part1 - SOLUTION FOR ASSIGNMENT 6 PART 1(1 Solution...

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