Embedded Options and Effective Duration
For bonds that have embedded options, such as putable and callable bonds, Modified duration will not correctly approximate the price move for a change in yield.
To price such bonds, one must use option pricing to determine the value of the bond, and then one can compute its delta (and hence its lambda), which is the duration. The effective duration is a discrete approximation to this latter, and depends on an option pricing model.
Consider a bond with an embedded put option. As an example, a $1,000 bond that can be redeemed by the holder at par at any time before the bond's maturity (i.e. an American put option). No matter how high interest rates become, the price of the bond will never go below $1,000 (ignoring counterparty risk). This bond's price sensitivity to interest rate changes is different from a non-puttable bond with otherwise identical cashflows. Bonds that have embedded options can be analyzed using "effective duration". Effective duration is a discrete approximation of the slope of the bond's value as a function of the interest rate.
where Δ y is the amount that yield changes, and
are the values that the bond will take if the yield falls by y or rises by y, respectively. However this value will vary depending on the value used for Δ y.
Read more about this topic: Bond Duration
Famous quotes containing the words embedded, effective and/or duration:
“The idea of feminine authority is so deeply embedded in the human subconscious that even after all these centuries of father-right the young child instinctively regards the mother as the supreme authority. He looks upon the father as equal with himself, equally subject to the woman’s rule. Children have to be taught to love, honor, and respect the father.”
—Elizabeth Gould Davis (b. 1910)
“I know no method to secure the repeal of bad or obnoxious laws so effective as their stringent execution.”
—Ulysses S. Grant (1822–1885)
“Higher than the question of our duration is the question of our deserving. Immortality will come to such as are fit for it, and he would be a great soul in future must be a great soul now.”
—Ralph Waldo Emerson (1803–1882)