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Hull Series : Duration and Convexity PDF Print E-mail
Written by FemiByte   
Tuesday, 29 September 2009 12:36

In this article, we discuss duration and convexity of bonds.

 

Duration

Intuitively, the duration of a bond is how long on average the holder of the bond has to wait before receiving cash payments. Formally the duration is the percent change in a bond's price with respect to yield. It measures the sensitivity of the bond's price to interest rate movements.

The price of a bond B is given by

The duration is given by

 

We can rewrite D as

=>

 

The negative of the 1st derivative of the bond price

is known as the Dollar Duration (DD) and is the absolute change in the bond's price with respect to the yield.

Modified Duration

If y is expressed with a compounding frequency of m times per year, instead of the continuous assumption as above, then we have

We then define the modified duration as

 

DV01

Risk is often measured as the dollar value of a basis point (DV01):

where 0.0001 repreesents 1 basis point or one-hundredth of 1 percent.

 

Convexity

The convexity is a measure of the sensitivity of the duration of a bond with respect to a change in interest rates. It is a measure of the 2nd derivative of the bond price with respect to the interest rate.

The convexity is given by


 

We can obtain the Taylor expansion for the change in the price of the bond, which is:

 

Last Updated on Friday, 01 January 2010 22:36
 

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