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
	t₀	t₁	t₂	t₃
One-year rate	1.330%	???	???	???
Two-year rate	1.590%	???	???
Three-year rate	1.810%
Four-year rate	2.030%

Implied forward 1 year rate_t+1f_{1 X}			at time t+1 (in one year)

Implied forward 1 year rate_t+2f_{1 x}			at time t+2 (in two years)

Implied forward 2 year rate_t+1f_{2 x}			at time t+1 (in one year)

Implied forward 1 year rate_t+3f_{1 x}			at time t+3 (in three years)

Implied forward 2 year rate_t+2f_{2 x}			at time t+2 (in two years)

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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