Question

Forward rates you have the following assumptions and spot rates - solve for the implied forward rates 0.680% 1.120% 1.210% One-year rate Two-year rate five-year rate Implied forward 5 year rates ??? Forward rates you have the following assumpitons and spot rates - solve for the implied forward rates One-year rate Two-year rate ??? 0.680% 0.860% Implied forward 1 year rate.fi in one year Forward rates you have the following assumptions and spot rates - solve for the implied forward rates to Two-year rate Four-year rate 1.360% 1.660% ??? Implied forward 2 year rate 2f1 in two years

Answer 1

Since multiple questions are asked answer to the first question is provided as HOMEWORKLIB's guidelines.

Given information:

one year rate = ₀F₁ = 0.680%

Two year rate, one year from now = ₁F₂ = 1.120%

Two year rate, three years from now = ₃F₂ = 1.210%

To satisfy no arbitrage condition,

an investor investing for 5 years from now is equivalent to

the investor investing in one year bond, then invest the proceeds for two years one year from now and subsequently invest the proceeds for 2 years 3 years from now.

Five year rate = ₀F₅

Assuming we invest $1 in both conditions then

1*e^₀F₅*5 = 1*e^₀F₁*1 * e^₁F₂*2 * e3^F₂*2 = 1 *  e(^{s1*1 + ₁F₂*2 +} 3^F₂*2)

Since the base is "e" on both sides, we can equate the powers:

₀F₅*5 = ₀F₁*1 + ₁F₂*2 + ₃F₂ * 2 = 0.680 * 1 + 1.120 * 2 + 1.210 * 2 = 5.34%

hence ₀F₅ = 5.34 / 5 = 1.068

Now to calculate ₁F₅, we apply no arbitrage condition again which is an investor investing for 5 years is equivalent to

the investor investing in one year bond, then invest the proceeds for five years one year from now

Assuming we invest $1 in both conditions then

1*e^₀F₅*5 = 1*e^₀F₁*1 * e^₁F₅*4

Since the base is "e" on both sides, we can equate the powers:

₀F₅ * 5 = ₀F₁*1 + ₁F₅*4

1.068 * 5= 0.0680 + ₁F₅ *4

Hence ₁F₅ = (1.0680 * 5- 0.680) / 4 = 1.165 %

Answer: Implied forward 5 year rate = 1.165%