Question

In: Finance

you have the following assumptions and spot rates - solve for the implied forward rates

you have the following assumptions and spot rates - solve for the implied forward rates

t0t1t2t3
One-year rate1.330%?????????
Two-year rate1.590%??????
Three-year rate1.810%


Four-year rate2.030%


Implied forward 1 year ratet+1f1 X   
at time t+1 (in one year)





Implied forward 1 year ratet+2f1 x
at time t+2 (in two years)





Implied forward 2 year ratet+1f2 x
at time t+1 (in one year)





Implied forward 1 year ratet+3f1 x
at time t+3 (in three years)





Implied forward 2 year ratet+2f2 x
at time t+2 (in two years)

Solutions

Expert Solution

(1 + 2 year spot rate)2 = (1 + 1 year spot rate) * (1 + Implied forward 1 year rate t+1f1)

(1 + 1.590%)2 = (1 + 1.330%) * (1 + Implied forward 1 year rate t+1f1)

(1 + Implied forward 1 year rate t+1f1) = (1 + 1.590%)2 / (1 + 1.330%)

(1 + Implied forward 1 year rate t+1f1) = 1.01851

Implied forward 1 year rate t+1f1 = 1.851%

(1 + 3 year spot rate)3 = (1 + 2 year spot rate)2 * (1 + Implied forward 1 year rate t+2f1)

(1 + 1.810%)3 = (1 + 1.590%)2 * (1 + Implied forward 1 year rate t+2f1)

(1 + Implied forward 1 year rate t+2f1) = (1 + 1.810%)3 / (1 + 1.590%)2

(1 + Implied forward 1 year rate t+2f1) = 1.02251

Implied forward 1 year rate t+2f1 = 2.251%

(1 + 3 year spot rate)3 = (1 + 1 year spot rate) * (1 + Implied forward 2 year rate t+1f2)2

(1 + 1.810%)3 = (1 + 1.330%) * (1 + Implied forward 2 year rate t+1f2)2

(1 + Implied forward 2 year rate t+1f2)2 = (1 + 1.810%)3 / (1 + 1.330%)

(1 + Implied forward 2 year rate t+1f2)2 = 1.04144

(1 + Implied forward 2 year rate t+1f2) = (1.04144)(1 / 2)

(1 + Implied forward 2 year rate t+1f2) = 1.02051

Implied forward 2 year rate t+1f2 = 2.051%

(1 + 4 year spot rate)4 = (1 + 3 year spot rate)3 * (1 + Implied forward 1 year rate t+3f1)

(1 + 2.030%)4 = (1 + 1.810%)3 * (1 + Implied forward 1 year rate t+3f1)

(1 + Implied forward 1 year rate t+3f1) = (1 + 2.030%)4 / (1 + 1.810%)3

(1 + Implied forward 1 year rate t+3f1) = 1.02693

Implied forward 1 year rate t+3f1 = 2.693%

(1 + 4 year spot rate)4 = (1 + 2 year spot rate)2 * (1 + Implied forward 2 year rate t+2f2)2

(1 + 2.030%)4 = (1 + 1.590%)2 * (1 + Implied forward 2 year rate t+2f2)2

(1 + Implied forward 2 year rate t+2f2)2 = (1 + 2.030%)4 / (1 + 1.590%)2

(1 + Implied forward 2 year rate t+2f2)2 = 1.05005

(1 + Implied forward 2 year rate t+2f2) = (1.05005)(1 / 2)

(1 + Implied forward 2 year rate t+2f2) = 1.02472

Implied forward 2 year rate t+2f2 = 2.472%

jeff jeffy answered 2 years ago
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