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12. (Pure duration o) It is sometimes useful to introduce variations of the spot rates that are different from an additive variation. Let s =
12. (Pure duration o) It is sometimes useful to introduce variations of the spot rates that are different from an additive variation. Let s = (s, s, sg...., s) be an initial spot rate sequence (based on m periods per year). Let s(x) = (51, 82, ..., s.) be spot rates s 42 parameterized by 2, where 1 + $x/m = e/*(1 + $/m) for k = 1,2,...,n. Suppose a bond price PQ), is determined by these spot rates. Show that IdP Pd is a pure duration, that is, find D and describe it in words, 12. (Pure duration o) It is sometimes useful to introduce variations of the spot rates that are different from an additive variation. Let s = (s, s, sg...., s) be an initial spot rate sequence (based on m periods per year). Let s(x) = (51, 82, ..., s.) be spot rates s 42 parameterized by 2, where 1 + $x/m = e/*(1 + $/m) for k = 1,2,...,n. Suppose a bond price PQ), is determined by these spot rates. Show that IdP Pd is a pure duration, that is, find D and describe it in words
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