Question

2. You have the following incomplete information on yields, forward rates from time t-1 to t, and prices (risk-free, zero-coupon bonds with face amount $100):

Maturity	Yield	Price	Forward Rate
1		P1=98.00
2			f2=2.50%
3	y3=2.50%

Given this information, what is the price of a 3-year, 5%, annual-pay, coupon bond with face amount $1,000? (Please fill in the table as well.)

Answer 1

Price of zero coupon bond = Face Value / (1 + r)ⁿ

R = Yield

Forward Rate (in year 1) = Yield (in year 1) = 2.04%

Yield₂ = {[(1 + Forward Rate₁) * (1 + Forward Rate₂)]^(1/2)} - 1
= [(1.024 * 1.025)^(1/2)] - 1
Yield₂ = 2.27%

(1 + Yield₃)³ = [(1 + Forward Rate₁) * (1 + Forward Rate₂) * (1 + Forward Rate₃)]
Forward Rate₃ = {(1 + Yield₃)³ / [(1 + Forward Rate₁) * (1 + Forward Rate₂)]} - 1
= [(1.025)³ / (1.024 * 1.025)] - 1
= 2.96%

Price of Bond = Coupon₁ / (1 + Yield₁)¹ + Coupon₂ / (1 + Yield₂)² + (Coupon₃ + Face Value) / (1 + Yield₃)³