Revision as of 01:18, 20 November 2023 by Admin (Created page with "Determine which of the following expressions represents the modified duration for a zero-coupon bond that is currently priced at an annual effective yield rate i and an n-year maturity. <ul class="mw-excansopts"><li><math display = "block">n</math></li><li><math display = "block">n(1+i)</math></li><li><math display = "block">n(1+i)^{-1}</math></li><li><math display = "block">\frac{\sum_{t=1}^nt(1+i)^{-t}}{\sum_{t=1}^n(1+i)^t}</math></li><li><math display = "block">\frac...")
Nov 20'23
Exercise
Determine which of the following expressions represents the modified duration for a zero-coupon bond that is currently priced at an annual effective yield rate i and an n-year maturity.
- [[math]]n[[/math]]
- [[math]]n(1+i)[[/math]]
- [[math]]n(1+i)^{-1}[[/math]]
- [[math]]\frac{\sum_{t=1}^nt(1+i)^{-t}}{\sum_{t=1}^n(1+i)^t}[[/math]]
- [[math]]\frac{\sum_{t=1}^nt(1+i)^{-t}}{\sum_{t=1}^n(1+i)^{-t}}[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
Nov 20'23
Solution: C
[[math]]
{D}_{\mathrm{mod}}=-\frac{\frac{d}{d i}(1+i)^{-n}}{(1+i)^{-n}}=\frac{n(1+i)^{-n-1}}{\displaystyle{(1+i)^{-n}}}=n(1+i)^{-1}
[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.