pj
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The classical approach to the Greek calculation is
"bump and reprice". One bumps a quote, re-calibrates and
reprices. Reprice and repeat.
Now I am told about this technique which is seemingly widely used in various banks.
Jacobians.
Basically, one estimates the first matrix in the expression
using them.
Does anyone have any concrete info on that?
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The older I grow, the more I distrust the familiar doctrine that age brings wisdom
Henry L. Mencken |
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I've used a similar approach to do a "risk rotation" from one set of parameters to another
the basic idea is quite simple
if I represents your instruments vector
and x represents your model parameters vector
dI/dx matrix is quick/stable to calculate as doesn't require recalibration (just bump each element of x and reprice)
dx/dI is more difficult as it does, so you just invert dI/dx (checking it is well conditioned, I suppose)
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nikol
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Can be used also in ir-curve <-> ivol-cube scenarios etc.
However, don't you have to calculate each cross-element of the matrix? This makes whole thing less optimal. |
... What is a man
If his chief good and market of his time
Be but to sleep and feed? (c) |
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pj
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I should make myself more clear.
Any written sources? |
The older I grow, the more I distrust the familiar doctrine that age brings wisdom
Henry L. Mencken |
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mtsm
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Everybody has been using this for decades. Among others to map zero risks to market risks, as well as what others described here. BGM vega used to be one big pain in the butt where that would be hard to get right, but who cares about BGM nowadays...
Since it is just an application of multi-variable calculus or functional calculus if you consider continuous curves, people just work it out to fit their needs. There must be internal working papers. Those who publish don't often consider this essential application and prefer wasting their time on other curve buildnig aspects.
BTW, in a multi-curve world with various bases there are then also more subtle considerations I think.
Google search: "interest rate" risk jacobian
http://www.closemountain.com/papers/risktransform1.pdf
https://quant.opengamma.io/Sensitivity-Computation-OpenGamma.pdf
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pj
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Thank you, mtsm.
Now everything is clear.
Our R&D was punting Jacobians as a general new new approach.
(With some cryptic remarks which make sense now)
Whereas it is used in the interest rates.
Thus my googling was futile. |
The older I grow, the more I distrust the familiar doctrine that age brings wisdom
Henry L. Mencken |
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ronin
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The key word is "automated differentiation". There is even a book with that title. And a ton of papers. And even software providers.
It's many things, but it isn't new. |
"There is a SIX am?" -- Arthur |
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I am interested in practical problems that could arise from using this methodology:
- slow computing time (in the sense that one of the computation steps is very slow compare to the other ones)?
- numerical instability:
* inversion of the Jacobian?
* due to the interpolation of the curve representation (for example IR curve interpolated with splines)?
- or any other problem.
Feel free to reply to me privately. |
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