David M. Harrison, Ph.D.

1
Mortgage Price Volatility

• Review of the Price-Yield Relationship
• An increase (decrease) in the required yield
• Price Volatility Characteristics of Mortgages

2
Determinants of Price Volatility

• Characteristics of a Mortgage that Affect Its
  Price Volatility
• Coupon Rate
• Term to Maturity
• Yield-to-Maturity

3
Measuring Mortgage Price Volatility

• Price Value of a Basis Point
• Note Mortgage Yield Ticks Usually Equal 1/8th of
  1

4
Duration

• Definition -
• Derivation

5
Calculating Duration

• Ex. Consider a 100,000, 6 APR mortgage with 10
  years to maturity and an initial yield of 8.0.
  What is this mortgages duration?

6
Alternative Duration Derivation

• Rewrite the price of a mortgage as the present
  value of an annuity
• Differentiate with respect to the required yield
• Modified Duration

7
Now What???

• Approximate Change in Price
• Actual Change in Price
• Conclusions

8
Duration Illustrated

• Duration attempts to measure
• Conclusions

Price
Yield
9
Approximating Duration

• Approximating a Mortgages Duration
• Example What is the approximate duration for
  our 10 year, 6 APR, 100,000 mortgage with 10
  years remaining until maturity and an initial
  yield of 8.0?

10
What About Embedded Options???