Question

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%

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

Answer 1

A. Market Yield is 5% P.A
Monthly payment = (Principal * Rate of interest * (1+Rate on interest)^96)/((1+Rate on interest)^96)-1)
= ((10,00,000 * .004167 * 1.004167^96)/(1.004167^96 - 1)
= ((10,00,000) * .004167 * 1.490633) / (1.490633 - 1)
= ((10,00,000 *.006211) / 0.490633
= 6210.971/0.490633
Monthly payment =	12659.1
B. Market Yield is 6% P.A
Monthly payment = (Principal * Rate of interest * (1+Rate on interest)^96)/((1+Rate on interest)^96)-1)
= ((10,00,000 * .005833 * 1.005833^96)/(1.005833^96 - 1)
= ((10,00,000) * .005833 * 1.614143) / (1.614143 - 1)
= ((10,00,000 *.008071) / 0.614143
= 8070.714/0.614143
Monthly payment =	13141.42
C. Market Yield is 7% P.A
Monthly payment = (Principal * Rate of interest * (1+Rate on interest)^96)/((1+Rate on interest)^96)-1)
= ((10,00,000 * .005 * 1.005^96)/(1.005^96 - 1)
= ((10,00,000) * .005 * 1.757966) / (1.757966 - 1)
= ((10,00,000 *.010255) / 0.757966
= 10254.80/0.757966
Monthly payment =	13529.37