Forums > Risk Management > Jacobians in risk management

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 pj Total Posts: 3669 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 andreprices. 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 expressionusing 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: 1458 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 anotherthe basic idea is quite simpleif I represents your instruments vectorand x represents your model parameters vectordI/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: 1483 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. ... What is a man If his chief good and market of his time Be but to sleep and feed? (c)
 pj Total Posts: 3669 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: 255 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 jacobianhttp://www.closemountain.com/papers/risktransform1.pdfhttps://quant.opengamma.io/Sensitivity-Computation-OpenGamma.pdf
 pj Total Posts: 3669 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
 ronin Total Posts: 708 Joined: May 2006
 Posted: 2021-01-15 15:44 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
 BlackSwan Total Posts: 31 Joined: Dec 2006
 Posted: 2023-01-08 09:58 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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