Question

Thee 3-month zero rate is 6% and the 9-month zero rate is 6.5%. What is the forward rate for the period between 3month and 9month?

*Note : all rates here are continuously compounded.

Choose from the following options.

7.25%

7.50%

7.00%

6.75%

Answer 1

Forward Rate for 6 months, 3 months from now = 9-month rate / 3-month rate

e^{[r * (6/12)]} = e^{[0.065 * (9/12)]} / e^{[0.06 * (3/12)]}

e^{[r * 0.5]} = e^[0.04875] / e^[0.015]

e^{[r * 0.5]} = 1.05 / 1.015

e^{[r * 0.5]} = 1.0343

[r * 0.5] * log(e) = log(1.0343)

[r * 0.5] * 1 = 0.03375

r = 0.03375 / 0.5 = 0.0675, or 6.75%

Hence, 4th Option is correct.