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In order to calculate the bucket wise sensitivities of an arbitrary derivative one has to blip the inputs of the yield curve construction process (i.e. bootstrapping) and recalculate the price of the derivative again. I'd like to know if there is an easier way to get those sensitivities without performing the bootstrapping again and again. What I mean is the following:Calculating the sensitivities means calculating the gradient of which is. Here are the par swap rates.Is it possible to 'freeze' the Jacobian, so that one can omit several bootstrapping processes?I appreciate any hint, thanks in advance.

QuoteOriginally posted by: BustopherJonesIs it possible to 'freeze' the Jacobian, so that one can omit several bootstrapping processes?The answer seems to be in the question. When you calibrate your curves (bootstrapping or otherwise), you compute the Jacobian between the input market quotes (par rates, price, or spread) and the zero coupons curves (I guess you work in a multi-curves framework). As the curves are simple instruments you should have an explicit computation of the derivatives (for example using algorithmic differentiation). The computation of the full Jacobian should not take more than 2 or 3 times the curve construction time (even if there are 20 points on the curve).For what I know, most of the (professional) systems work in that way. Even if most of them have problems of some type in computing real multi-curve to multi-curve Jacobian.

> In order to calculate the bucket wise sensitivities of an arbitrary derivative one has to blip the inputs of the yield curve construction process (i.e. bootstrapping) and recalculate the price of the derivative again. That is not true. Bumping inputs creates sensitivities to the curve generation process in addition to derivative sensitivities. An alternative is to apply bucket shocks to the set of output discount factors (discussed here).

The Hagan and West paper, "Interpolation Methods for Curve Construction", Appl Math Finance, 2006 has some discussion on the localness of hedge recommendations. There are examples of classic bump inputs and revalue as you describe and the alternative of perturbing forward curve and computing equivalent hedges described in the other thread.The paper is available online at finmod

Thanks for your helpful remarks!

Recently I also made some calculations to test the gradient/Jacobian approach mentioned by Bustopher. In fact, it worked quite well. The sensitivity based on zero rate shifts looks good for the entire curve (i.e. parallel shift), but the bucketwise sensitivities are far from accurate. Using the Jacobian instead, freezing it and subsequently multiplying with the gradient yields reasonable approximations on the buckets as well.However, the question arises at which frequency you should "update" the Jacobian. Intuitively I would imagine that changes should not be that dramatic while it may also depend on market volatility. Do you have some suggestions/experiences regarding that point? Thanks for your comments.