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pj


Total Posts: 3558
Joined: Jun 2004
 
Posted: 2020-11-06 14:59
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?

The older I grow, the more I distrust the familiar doctrine that age brings wisdom Henry L. Mencken

silverside


Total Posts: 1425
Joined: Jun 2004
 
Posted: 2020-11-06 15:09
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)


nikol


Total Posts: 1237
Joined: Jun 2005
 
Posted: 2020-11-06 18:22
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.

pj


Total Posts: 3558
Joined: Jun 2004
 
Posted: 2020-11-06 21:42
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

mtsm


Total Posts: 254
Joined: Dec 2010
 
Posted: 2020-11-06 22:22
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



pj


Total Posts: 3558
Joined: Jun 2004
 
Posted: 2020-11-07 12:52
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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