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)