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cprasad
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Posts: 6
Joined: September 9th, 2016, 3:47 am

Duration in Vasicek model

August 9th, 2021, 1:54 pm

How do you calculate duration of a zero-coupon bond in short-rate models such as Vasicek model? 

If you compute duration as the sensitivity w.r.t. yield of the bond, the duration would be
equal to T, the time-to-maturity no matter which model you use. But if it is w.r.t. the short rate
then it would depend on the model. 
I want to know what is the accepted definition for duration of a zero. May be, it's the sensitivity 
w.r.t. yield.
Can somebody suggest a book or paper that clarifies this?
 
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Alan
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Re: Duration in Vasicek model

August 9th, 2021, 4:04 pm

I think wikipedia is reliable here: [$]\Rightarrow[$] T (for all ZCB's)
 
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bearish
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Joined: February 3rd, 2011, 2:19 pm

Re: Duration in Vasicek model

August 9th, 2021, 8:37 pm

There are two separate questions lurking here. The simple one has been asked and answered. The slightly more complicated (and, I’d argue, interesting) one is something like “what is a good measure of interest rate risk for a zero coupon bond?” The latter is definitely model dependent. Or, in the absence of an explicit model, can be made data dependent via PCA or similar statistical methods. In a one-factor model, there is a unique answer up to scaling. In a more realistic setting, we tend to start with a set of key rate durations (or, equivalently, a set of partial dv01s) and then look for ways to group the exposures by factor.