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Term structure general note

A

actuary111

Member
When we are given the annual term structure in the form (6%,6%,6%,6%,7%) for a 5-year fixed interest security (like in Question 14.11), does the term structure represent the annual spot rates?

In other words, in this case, is the following true?
(6%,6%,6%,6%,7%)=(y1,y2,y3,y4,y5), where yt represents the t-year spot rate of interest.

So when we are given a term structure in this form, is it always made up of spot rates? Or are there any cases that the term structure will involve forward rates?

Any help would be greatly appreciated!

Thank you:)
 
Term structure represents the annual return on a n-yr ZERO-COUPON bonds. They are n-yr spot rates. You can use them to work out yield on bonds that do pay coupons.

To work out n-yr spot rates you need the current 1-yr spot rate and future 1-yr spot rates

y2 (2-yr spot rate) represents the annual return on a two year zero-coupon bond.

y2 = ((1+y1)(1+f11))^(1/2)

similarly:

y3 = ((1+y1)(1+f11)(1+f21))^(1/3), and so on...

y1 is current 1-yr spot rate
f11 is a fwd rate, it is 1-yr spot rate in 1 years time
f21 is 1 yr spot rate in 2 years time.


Good luck.
 
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