Question

Suppose that zero interest rates with continuous compounding are as follows: Maturity (months) 34 62 94 Rate % per annum) 3.02 3.22 3.42 3.5e 3.62 3.72 12e 152 18 Calculate forward interest rates for the second, third, fourth, fifth, and sixth quarters.

Answer 1

Given,

Zero interest rate with continuous compounding

Maturity (months)	Rate(% per Annum)
3	3.0
6	3.2
9	3.4
12	3.5
15	3.6
18	3.7

Forward rate can be calculated using

Forward rate (0,t,T)= ln(e^(r*T)/e^(r*t))/(T-t)

So, forward interest rate for 2nd quarter rate = ln(e^(0.032*0.5)/e^(0.03*0.25))/(0.5-0.25) = 3.40%

forward interest rate for 3rd quarter rate = ln(e^(0.034*0.75)/e^(0.032*0.5))/(0.75-0.5) = 3.80%

forward interest rate for 4th quarter rate = ln(e^(0.035*1)/e^(0.034*0.75))/(1-0.75) = 3.80%

forward interest rate for 5th quarter rate = ln(e^(0.036*1.25)/e^(0.035*1))/(1.25-1) = 4.00%

forward interest rate for 6th quarter rate = ln(e^(0.037*1.5)/e^(0.036*1.25))/(1.5-1.25) = 4.20%