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Topic Title: DV01 Calculation
Created On Tue Oct 02, 12 05:38 PM
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kgdakid21
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Tue Oct 02, 12 05:38 PM
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Hi Guys I am and FX guy and trying to wrap my head around DV01. I understand this is a simple question but would appreciate the help. DV01 on a swap is the change in PV relative to a 1bp shift in yield. I am being told it is best calculated as the sum of the discount factors. So in US IRS you can utilize Libor for short curve and par rates for the long curve and get your discount factors w/ 1/(1+Libor/Par Rate + Act/360). So in theory you are going to get a number that is .99.......... So lets say their are 20 periods of a swap and my DV01 is ~20? It doesn't quiet make sense to me.

 
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karfey
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Thu Oct 04, 12 04:24 PM
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Let's go back to principles on this one. Since you have already defined DV01 to be the change in PV relative to an incremental shift in yield, we should utilize simple calculus to compute DV01.

For a simple cashflow N at time t, discounted by the yield exp(-zt), where z is the yield,
we have PV = N*exp(-zt)
So, d(PV)/dz = -t*N*exp(-zt)

It is as simple as that.

Now, we apply the same logic to a swap. Assume a 1-year fix-floating swap. We know the floating legs can be decomposed into 2 nominal flows, one at t=0, and another at t=1yr. So evaluating the DV01 is simply a matter of applying the d(PV)/dz at the appropriate time periods. The value of DV01 is only meaningful with a time period (duration) attached to it. We can sum up the DV01 by their duration, and hedge away interest rate risk according to this duration.
 
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DavidJN
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Fri Oct 05, 12 06:17 PM
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kgdakid21, you are actually not far at all from getting it. You need to sum the accrual-weighted discount factors to get the DV01. By accrual-weighting, I mean multiplying the discount factor at each payment date by the year fraction used to determine the dollar fixed side payment at that date. The accrual fractions will be approximately 0.5 for semi-annual pay swaps and around 0.25 for quarterly pay, etc. (exact numbers depend on the day count fraction used).
 
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wickedwit
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Sun Oct 14, 12 05:46 PM
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I find the effective duration formula to be most intuitive as roughly the average change in price for a certain interest rate change: So (Price (yield down) - Price (yield up)) / (2 x (initial price) x (yield change))

For DV01 just use Notional x $ duration (years) x 1 bps, so for example:

As a note in general for treasuries and swaps (on the run swaps generally have a price of $100 so its the same), but make sure you use $ duration and not just modified or something so dollar duration is:

(mod/effective etc.)yrs x px/100 = $ duration

$100mm x 6 x 1bps = $60k = dv01
 
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Panoramix
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Tue Oct 16, 12 02:17 PM
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I got a quick question about it, just to have a double check and understand if i understood the overall speech.

Suppose i have the following position:short on 2 years bond and long on 10 years bond, for which the respective dollar value per BPS at a mid price is 0.0175 and 0.0708 (BBG field is DOLLAR_VALUE_PER_BP_MTY_MID). Moreover suppose that i have a 98.5bps swing and a notional amount of 1 million.
In order to compute my profit and loss i just need to apply what you told us:

(0.0708-0.0175)*98.5*1M/100=525K


Did i get the right concept?

EDIT: should i also take into account the time in the same way i compute the value for the future on the Euribor?

-------------------------
"Nowadays people know the price of everything and the value of nothing." The Picture of Dorian Grey (1891)

Edited: Tue Oct 16, 12 at 02:55 PM by Panoramix
 
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wickedwit
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Sat Oct 27, 12 09:11 PM
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if you were long 1mm of one and short 1mm of the other, you have the right concept but the wrong decimal place. Think about what you have here: a dvo1 of .0175 and .0708 is really a dollar duration of 1.75 and 7.08 divided by 100. So 525k is way too much if 100bps moves the 10yr only 7.08 points or 7.08%. The number 52.5k
 
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LucasGomez
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Mon Oct 29, 12 05:59 AM
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Hey kgdakid21

Maybe you could check out my post in the General Forum (here's the Link: http://www.wilmott.com/messageview.cfm?catid=3&threadid=92629) I was looking for an answer to Rho greek computation on a eurpean FXO and I posted some formulae on DV01 that maybe you could find useful.

To me DV01 is any sort of analysis that involves finding out the expected change in an asset's market value given a small change in interest rates. As with everything in life, there are several ways of looking at things and solving questions, hence not being this the exception you'll find that there are several ways of computing DV01.

For the sake of clarity say you've got a fixed-floating IRS, from it you could derive either analytically (e.g. Partial derivatives) or based on simulation (e.g. stressing parameters and finite differences after) several values of interest rate sensitivity or DV01, these are:

1) "Expected change of each leg's MV based on":

- a +/- 0.01 shift of their equivalent yields.
- a +/- 0.01 shift of the interpolated zero coupon rates applicable to each flow date.
- a +/- 0.01 shift of the nodes of the relevant zero coupon curves (either One by One, the curve as a whole or buckets/Sections of it).
- a +/- 0.01 shift of the nodes of the relevant Par/Market curves (either one by one, the curve as a whole or buckets/Sections of it).

2) "Expected change of the floating leg MV based on":

- a +/- 0.01 shift of the interpolated zero coupon rates associated to the implied forward rate computation.
- a +/- 0.01 shift of the nodes of the relevant zero coupon curves associated to the implied forward rate computation.
- a +/- 0.01 shift of the nodes of the relevant Par/Market curves associated to the implied forward rate computation.
- a +/- 0.01 shift of the index value at the coming fixing date.

As you can see its possible to compute various risk figures based on the discounting, the index forwarding, the interpolation methodology, the computing approach, FX forwarding (not treated above but still there) etc..

I'm curious to know, you being an FX guy didn't you analyze DV01 on FX forward positions?

Also, I recomend reading Thomas Ho on "Key Rate Durations (KRD)" you can google it or find it at IIJ.

Hope it helped!

best,


-------------------------
Lucas M. Gomez
 
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Panoramix
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Mon Oct 29, 12 04:14 PM
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Quote

Originally posted by: wickedwit
if you were long 1mm of one and short 1mm of the other, you have the right concept but the wrong decimal place. Think about what you have here: a dvo1 of .0175 and .0708 is really a dollar duration of 1.75 and 7.08 divided by 100. So 525k is way too much if 100bps moves the 10yr only 7.08 points or 7.08%. The number 52.5k


Hi wickedwit.

Thanks a lot for your feedback, i really appreciated it. I also supposed that the overall return was too much, but better to have also someone else's point of view.



-------------------------
"Nowadays people know the price of everything and the value of nothing." The Picture of Dorian Grey (1891)
 
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