Question

the two year zero rate is 6 and the three year zero rate is 6.5%. what is the 1-year forward rate after the second year?! assume continuous compounding

Answer 1

We compute the 1-year forward rate after second year to third year with following equation:

$\large e^{r_2*2}*e^{f_{2,3}^{1}*1} = e^{r_3*3}$

where,

r = zero rate

f = forward rate

putting the values:

$\large e^{0.06*2}*e^{f_{2,3}^{1}*1} = e^{0.065*3}$

$\large e^{f_{2,3}^{1}} = \frac{e^{0.065*3}}{e^{0.06*2}}$

$e^{f_{2,3}^{1}} = \frac{1.21531098648973}{1.12749685157938}$

$e^{f_{2,3}^{1}} = 1.07788415088463$

$f_{2,3}^{1} = 1.07788415088463-1$

$f_{2,3}^{1} = 0.07788415088463$

$\bg_green \large f_{2,3}^{1} = 7.79\%$

Thus, 1-year forward rate from 2nd year to 3rd year = 7.79%

Hope this will help, please do comment if you need any further explanation. Your feedback would be highly appreciated.