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A 30Y fixed rate mortgage is issued at 6% coupon rate. The loan is INTEREST ONLY (no amortization).

Expected payoff time is 8 Years or 96 months 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 the same, despite changes in market interest rate (96 months at 5%; 96 months at 6%, and 96 months @ 7% ). (5 points)

note: to calculate numerical duration at 6%, first price the loan 5%, 6% and 7% interest rate. Then calculate dollar duration as: (Price at 7% - price at 5%) / (7% -5%). Then divide the value above by price at 6% to get duration.

b. calculate numerical duration and convexity at 6% market interest rate based on pricing from 4a (5 points)

note: $convexity is the change in $dur, divided by change in interest rate. to calculate numerical convexity at 6%,

first calculate dollar duration at 6.5% location as: (price at 7% - price at 6%) / (7%-6%).

Then calculate the $dur at 5.5% location as: (price at 7% - price at 5%) / (6%-5%).

Then calculate the $con at 6% location as : ($dur at 6.5% - $dur at 5.5%) / (6.5% - 5.5%)

Last divide $convexity above by price at 6% to get convexity.

A 30Y fixed rate mortgage is issued at 6% coupon rate. The loan is INTEREST ONLY (no amortization).

Expected payoff time is 8 Years or 96 months 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 the same, despite changes in market interest rate (96 months at 5%; 96 months at 6%, and 96 months @ 7% ). (5 points)

note: to calculate numerical duration at 6%, first price the loan 5%, 6% and 7% interest rate. Then calculate dollar duration as: (Price at 7% - price at 5%) / (7% -5%). Then divide the value above by price at 6% to get duration.

b. calculate numerical duration and convexity at 6% market interest rate based on pricing from 4a (5 points)

note: $convexity is the change in $dur, divided by change in interest rate. to calculate numerical convexity at 6%,

first calculate dollar duration at 6.5% location as: (price at 7% - price at 6%) / (7%-6%).

Then calculate the $dur at 5.5% location as: (price at 7% - price at 5%) / (6%-5%).

Then calculate the $con at 6% location as : ($dur at 6.5% - $dur at 5.5%) / (6.5% - 5.5%)

Last divide $convexity above by price at 6% to get convexity.

A 30Y fixed rate mortgage is issued at 6% coupon rate. The loan is INTEREST ONLY (no amortization).

Expected payoff time is 8 Years or 96 months 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 the same, despite changes in market interest rate (96 months at 5%; 96 months at 6%, and 96 months @ 7% ). (5 points)

note: to calculate numerical duration at 6%, first price the loan 5%, 6% and 7% interest rate. Then calculate dollar duration as: (Price at 7% - price at 5%) / (7% -5%). Then divide the value above by price at 6% to get duration.

b. calculate numerical duration and convexity at 6% market interest rate based on pricing from 4a (5 points)

note: $convexity is the change in $dur, divided by change in interest rate. to calculate numerical convexity at 6%,

first calculate dollar duration at 6.5% location as: (price at 7% - price at 6%) / (7%-6%).

Then calculate the $dur at 5.5% location as: (price at 7% - price at 5%) / (6%-5%).

Then calculate the $con at 6% location as : ($dur at 6.5% - $dur at 5.5%) / (6.5% - 5.5%)

Last divide $convexity above by price at 6% to get convexity.

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