Analysis of Fixed Income
Approx Duration
Francis Ng
1
Approximate Duration & Convexity
•
Modified duration is easily defined and computed when
cash flow is fixed.
•
What if the cash flows of the bond or security are highly
uncertain such as Mortgage Backed Securities (MBS)?
•
How do we measure or compute the duration of the MBS?
•
A practical approach for finding Modified Duration and
Convexity is to use the Approximate Duration and Convexity
method.
2
Approximate Duration & Convexity
We use the Approximation method:
Approximate duration =
P
-
- P
+
2P
0
(
∆
y)
Approximate convexity =
P
-
+ P
+
- 2P
0
P
0
(
∆
y)
2
where
P
-
denotes the price when yield declined by
∆
y
P
+
denotes the price when yield increased by
∆
y
P
0
denotes the initial price
∆
y denotes the small yield change
3
Approximate Duration & Convexity
