Q3. Spot rate, forward rate, and yield to maturity

One year zero priced at 5% yield. Two year 6% coupon bond priced at par. Three year 7% coupon par priced at par.

a. what is one year, two year AND three year spot rates (ie s1 s2 s3) (4 points)?

b. what is the 1 year and 2 year forward rate (ie f12 f23)? (4 points)

c. How much should a THREE year 10% coupon bond with face value of $1,000 be price at (4 points)?

d. What is the yield to maturity for bond in part 3c (4 points)?

4. Mortgage Pricing

A 30Y fixed rate mortgage is issued at 6% coupon rate. The loan fully amortizes over 30 year period.

Expected payoff time is 8 Years when initially issued. Assuming $1M in loan balance.

a. Price the loan today at 5%, 6%, and 7% market yield, assuming loan termination term stays constant with interest rate (96 months at 5%; 96 months at 6%, and 96 months @ 7% ). (4 points)

b. calculate numerical duration and convexity at 6% market interest rate based on pricing from 4a (4 points)

c. Price the loan today at 5%, 6%, and 7% yield, assuming loan termination term changes with interest rate (60 months at 5%; 120 months at 6%, and extends to 120 months @ 7% ). (4points)

d. calculate numerical duration and convexity at 6% market interest rate based on pricing from 4a (4 points)