Revision as of 00:26, 20 November 2023 by Admin (Created page with "The one-year forward rates, deferred t years, are estimated to be: {| class="table table-bordered" | Year (t) || 0 || 1 || 2 || 3 || 4 |- | Forward Rate || 4% || 6% || 8% || 10% || 12% |} Calculate the spot rate for a zero-coupon bond maturing three years from now. <ul class="mw-excansopts"><li>4%</li><li>5%</li><li>6%</li><li>7%</li><li>8%</li></ul> {{soacopyright | 2023 }}")
Nov 20'23
Exercise
The one-year forward rates, deferred t years, are estimated to be:
| Year (t) | 0 | 1 | 2 | 3 | 4 |
| Forward Rate | 4% | 6% | 8% | 10% | 12% |
Calculate the spot rate for a zero-coupon bond maturing three years from now.
- 4%
- 5%
- 6%
- 7%
- 8%
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
Nov 20'23
Solution: C
[[math]]
\begin{array}{c}{{s_1=_{1}f_{0} = 0.04 }}\\ {{_{1}f_{1}=0.06=\frac{\left(1+s_{2}\right)^{2}}{\left(1+s_{1}\right)^{2}}-1\Rightarrow s_{2}=\sqrt{(1.06)(1.04995)^{2}})^{1/3}-1=0.04995}}\\ {{\mathrm{}_{1}f_{2}=0.08=\frac{\left(1+s_{2}\right)^{2}}{\left(1+s_{2}\right)^{2}}-1\Rightarrow s_{3}=\mathrm{}\left((1.08\right)(1.04995)^{2}-1=0.05987=6\%.}}\end{array}
[[/math]]
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.