Bond duration: Encyclopedia II - Bond duration - Embedded options and effective duration

Bond duration - Embedded options and effective duration

For bonds that have embedded options, Macauley duration and modified duration will not correctly approximate the price move for a change in yield. 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 points before the bond's maturity. No matter how high interest rates become, the price of the bond will never go below $1,000. This bond's price sensitivity to interest rate changes is different than a non-puttable bond with identical cashflows. Bonds that have embedded options should 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 Δy is the amount that yield changes, and V _{− Δy}andV _{+ Δy} are the values that the bond will take if the yield falls by y or rises by y, respectively.

Adapted from the Wikipedia article "Embedded options and effective duration", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki