The SABR Greeks do not show the distribution of the risk along the strike dimension. Therefore, the presentation of the risk using a Vega Cube containing a strike dimension is desirable. The direct calculation of the Vega Risk Cube for exotics however is impossible because the bumps of individual volatilities in the Cube cause the SABR model recalibration inconsistent with the model (the pricing models are callibrated to SABR and not to the strikes). How would one solve this? My approach is a given portfolio to construct an equivalent book of swaptions in order to match the SABR Greeks (ATM, á,â,ñ,volga, vanna) for each pair of the option maturity and the underlying in the SABR matrix. And then calculate the Vega Risk Cube for the equivalent book. The problem with this approach is how to make sure that the weights for the swaptions in the equivalent book are stable and unique. Any suggestions?

Hi,How are you calibrating your SABR parameters?Usually practice is to try to fit vanilla options under SABR to vanilla options under BS. By using this fitting process you should be able to build some sort of transformation matix for the risks.pabo

Often in pricing exotics, one calibrates the model not too the ATM swaptions/caplets but to swaptions and caplets which are struck at strikes that best represent the exotic ... There are a few different methods of selecting these swaptions/caplets depending on the exotic. Eg: selecting the fixed rate (strike) of the swaption so that the ration of the swaption's fixed leg to floating leg (where the legs inclcude the notional at the end date) matches the ratio for the exotic selecting the strike so that the same parallel shift of a yield curve which brings the exotic option to it's ATM point also brings the swaption to its ATM point selecting the swaption whose PV01's to parallel shifts and tilts of the yield curve matches the exotic'sIf this is done, then bumping the vol of each swaption/caplet gives the exotic's vega risk at a particular strikes, and these vega risks can be handled via SABR in the same manner as being long or short the swaption itself. (Alternatively, these swaptions/caplets often provide very stable hedges for the exotic, with less need for frequent re-balancing).If one cannot autocalibrate in this way, then one can use an external adjusters to move the risk to the proper strikes.I have a couple (pretty rough) drafts about this.

Hi Pat:Thanks! This is very useful. Are your papers (esp. on the external adjusters) available?Michael

yes ... send an email adress to me at phagan1@bloomberg.net and I can send a PDF version