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:
“It was your severed image that grew sweeter,
That floated, wing-stiff, focused in the sun
Along uncertainty and gales of shame
Blown out before I slept. Now you are one
I dare not think alive: only a name
That chimes occasionally, as a belief
Long since embedded in the static past.”
—Philip Larkin (1922–1986)
“Watteau is no less an artist for having painted a fascia board while Sainsbury’s is no less effective a business for producing advertisements which entertain and educate instead of condescending and exploiting.”
—Stephen Bayley (b. 1951)
“This pond never breaks up so soon as the others in this neighborhood, on account both of its greater depth and its having no stream passing through it to melt or wear away the ice.... It indicates better than any water hereabouts the absolute progress of the season, being least affected by transient changes of temperature. A severe cold of a few days’ duration in March may very much retard the opening of the former ponds, while the temperature of Walden increases almost uninterruptedly.”
—Henry David Thoreau (1817–1862)