Question

If I ask for a €1 million loan within 3 months with 3 month maturity, which will be the difference on interest payments if I lock today the interest rate using the 3x6 month Forward Interest Rate? 3 month Zero Coupon Rate: 3.5% 6 month Zero Coupon Rate: 3.7% 1 year Zero Coupon Rate: 4% 2 year Zero Coupon Rate: 4.5% 3 year Zero Coupon Rate: 5% If within 3 months, the 3 month Interest rate is 3% 1.335 2.-2165 3.500 4.0

Answer 1

The correct answer is the second option i.e. option 2 showing -2,165

3 month zero coupon rate = 3.5% = r3

6 month zero coupon rate = 3.7% = r6

Within 3 months, the 3 months forward interest rate = f

Hence, (1 + r3 / 4) x (1 + f / 4) = (1 + r6 / 2)

Hence, (1 + 3.5% / 4) x (1 + f / 4) = (1 + 3.7% / 2)

Hence, f = 4 x [(1 + 3.7% / 2) / (1 + 3.5% / 4) - 1] = 3.87%

Actual Within 3 months, the 3 months interest rate = z = 3%

Hence, the difference in interest payment = (z - f) x Loan amount x time period of 3 months = (3% - 3.87%) x 1,000,000 x 3 / 12 = - 2,165