Get started today!

Good to have you back!
If you've signed in to StudyBlue with Facebook in the past, please do that again.

Anonymous

Math 618 Answer to Selected Problems in Section 6.1 Autumn 2005 Problem 6.1.5 We want to find the spot rates i(2).5 , i(2)1 , i(2)1.5, and i(2)2 (where i(2)k = i0,k is the nominal rate of zero-coupon bond with maturity of k-year convertible semiannually). Let jk = i(2)k /2 be the corresponding effective half-year rate. Suppose the bonds face value and redemption amount are 100. • 12-year bond: (r = .02, j = .025) P Fr + F Using the actual yield, the price of the bond (at time 0) is P = (100 + 100r)vj = (100 + 2) 11 + .025 = 1021.025. Using the (effective half-year) spot rate j.5, the price is P = (100 + 100r)vj.5 = 1021 + j .5 . The (blue) prices are equal. So, 1021 + j .5 = 1021.025. Solving, we get j.5 = .025. (j.5 = .025) • 1-year bond: (r = .03, j = .05) P Fr = 3a27 j.5 Fr + F = 103a27 j1 Using the actual yield, the price of the bond (at time 0) is P = ···[F + F(r − j)an|j, or K + rj(F − K), or ···,]··· = 96.281179.... (N = 2, FV = 100, PMT = 3, and I/Y = 5% on a BA II PLUS gives PV = −96.28117914.) Using the (effective half-year) spot rate j.5 and j1, the price is P = Frvj.5 + (Fr + F)v2j1 = 31.025 + 103(1 + j 1)2 The (blue) prices are equal. So, 31.025 + 103(1 + j 1)2 = 96.281179. Solving, we get j1 = .050391825. (j.5 = .025, j1 = .050392) • 1 1/2-year bond: (r = .02, j = .075) P Fr = 2a27 j.5 Fr = 2a27 j1 Fr + F = 102a27 j1.5 Using the actual yield, the price of the bond (at time 0) is P = ···[F + F(r − j)an|j, or K + rj(F − K), or ···,]··· = 85.69710843 (N = 3, FV = 100, PMT = 2, and I/Y = 7.5% on a BA II PLUS gives PV = −85.69710843.) Using the (effective half-year) spot rate j.5, j1, and j1.5 the price is P = (Fr)vj.5 + (Fr)v2j1 + (Fr + F)v3j1.5 = 21.025 + 21.050392 + 102(1 + j 1.5)3 The (blue) prices are equal. So, 21.025 + 21.050392 + 102(1 + j 1.5)3 = 85.69710843. Solving, we get j1.5 = 0.07575521278. (j.5 = .025, j1 = .050392, j1.5 = .0757552) • 2-year bond: (r = .04, j = .075) P Fr = 4a27 j.5 Fr = 4a27 j1 Fr = 4a27 j1.5 Fr + F = 104a27 j2 Using the actual yield, the price of the bond (at time 0) is P = ···[F + F(r − j)an|j, or K + rj(F − K), or ···,]··· = 88.27735806 (N = 4, FV = 100, PMT = 4, and I/Y = 7.5% on a BA II PLUS gives PV = −88.27735806.) Using the (effective half-year) spot rate j.5, j1, j1.5, and j2 the price is P = (Fr)vj.5 +(Fr)v2j1 +(Fr)v3j1.5 +(Fr+F)v4j2 = 41.025 + 41.050392 + 41.07575523 + 104(1 + j 2)4 The (blue) prices are equal. So, 41.025 + 41.050392 + 41.07575523 + 104(1 + j 2)4 = 88.27735806. Solving, we get j2 = 0.07617249008. (j.5 = .025, j1 = .050392, j1.5 = .0757552, j2 = .0761725) Using i(2)k = 2jk, we have i(2).5 = 2j.5 = 5%, i(2)1 = 2j1 = 10.784%, i(2)1.5 = 2j1.5 = 15.151%, i(2).5 = 2j.5 = 15.2345%.

Advertisement
)

Advertisement

"StudyBlue is great for studying. I love the study guides, flashcards and quizzes. So extremely helpful for all of my classes!"

Alice , Arizona State University"I'm a student using StudyBlue, and I can 100% say that it helps me so much. Study materials for almost every subject in school are available in StudyBlue. It is so helpful for my education!"

Tim , University of Florida"StudyBlue provides way more features than other studying apps, and thus allows me to learn very quickly!Â I actually feel much more comfortable taking my exams after I study with this app. It's amazing!"

Jennifer , Rutgers University"I love flashcards but carrying around physical flashcards is cumbersome and simply outdated. StudyBlue is exactly what I was looking for!"

Justin , LSU