## Coupon curve duration, Financial Management

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Market price is used for determining the duration of a mortgage-backed security in the coupon curve duration. This approach to calculate the duration of mortgage-backed security was suggested by Douglas Breeden.  The coupon curve represents generic pass-through securities of a particular issuer with different coupon rates. Duration is obtained by the coupon curve of prices rolling up and down. The prices obtained from rolling up and down the coupon curve of prices are substituted into the duration formula.

Let us determine the coupon curve duration from the data given below:

 Coupon Price 7% 8% 9% 10% 11% 12% 82.19 88.06 93.38 97.34 101.19 111.23

Let us calculate the coupon curve duration for the 9% coupon pass-through. If the yield declines by 100 basis points, then we assume that the price of the 9% coupon pass-through will also increase to the price of the current 10% coupon pass-through. Similarly, if the yield of the 9% coupon passthrough increases by 100 basis points, the price would decrease to the price of the current 8% coupon pass-through. Therefore, the price would be 97.34 when there is a decline of 100 basis points in the yield while the price would be 88.06 when the yield increases by 100 basis points.

P0        =      93.38

P+        =      88.06

P-            =      97.34

Δy       =      0.01

The estimated duration is as follows:

Duration = 97.34 - 88.06

2(93.38)(0.01)

= 4.97.

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5/8/2014 1:38:10 PM

The correct estimated duration is:
Duration = (97.34 - 88.06) / 2(93.38)(0.01) = 4.332832