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Solution 1

# Solution 1 - Fin 448 Fixed-Income Securities Homework...

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Fin 448: Fixed-Income Securities Homework Solution 1 Wei Yang 1 Bootstrapping (1.1) ... (1.4) We solve the following equations by the iterative procedure 98 . 16 = p 0 . 5 100 99 . 50 = p 0 . 5 3 . 5 2 + p 1 (100 + 3 . 5 2 ) 103 . 31 = p 0 . 5 6 . 625 2 + p 1 6 . 625 2 + p 1 . 5 (100 + 6 . 625 2 ) 99 . 63 = p 0 . 5 4 . 25 2 + p 1 4 . 25 2 + p 1 . 5 4 . 25 2 + p 2 (100 + 4 . 25 2 ) which yield p 0 . 5 = 0 . 9816 , p 1 = 0 . 9610 , p 1 . 5 = 0 . 9377 , p 2 = 0 . 9156 and translate to y 0 . 5 = 3 . 75% , y 1 = 4 . 02% , y 1 . 5 = 4 . 34% , y 2 = 4 . 46% (1.5) The annualized, semi-annually compounded yield for the 2-year Treasury is found by solving 99 . 63 = 4 . 25 2 1 + y 2 1 + 4 . 25 2 1 + y 2 2 + 4 . 25 2 1 + y 2 3 + 100 + 4 . 25 2 1 + y 2 4 which yields y = 4 . 45% (1.6) The par coupon rate is determined from 1 = p 0 . 5 c 2 + p 1 c 2 + p 1 . 5 c 2 + . . . + p n 1 + c 2 to be c = 4 . 44% 1

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(1.7) If we switch to continuous compounding, the yields are computed from the prices by p k = e - y k k and so y 0 . 5 = 3 . 71% , y 1 = 3 . 98% , y 1 . 5 = 4 . 29% , y 2 = 4 . 41% 2 Arbitrage (2.1) Using the zero-coupon bond prices, the price of X is p 0 . 5 3 2 + p 1 3 2 + p 1 . 5 3 2 + p 2 (100 + 3 2 ) = 97 . 26 (2.2) The calculated price falls within the bid ask spread of the market quotes.
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Solution 1 - Fin 448 Fixed-Income Securities Homework...

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