# Swaption risk bucketing

In the IR swaption market, we have 24Expire10Tenor instruments(like a 2410 Matrix). Now I have the Vega number for each instrument, and I want to reduce the matrix size with the same total vega risk.

Matrix A(2410) to Matrix B(78), constrain by sum(A)=sum(B) Any hint for this problem? What method should I think about it? Thanks a lot!

• A(24*10) B(7*8)
– Tian
Commented Jun 23, 2022 at 11:05
• Hi Tian & welcome to QSE. Please clarify / re-format your question, because it is very unclear what exactly you're asking for. Commented Jun 23, 2022 at 11:18
• It sounds like you mark the implied volatility by various expiries of the swaptions, and by tenors of the underlying swaps, but not by moneyness. A 2d surface, rather than a 3d cube, is not great. The vol can vary a lot by moneyness. That observation aside, you then calculate sensitivities to bumping the vols that you merk. Now you want to rebucket these sensitivities to fewer buckets? Any reason why you can't just linearly allocate the undesired sensitivities to the nearest desired buckets? Are there more consideratios and constrains that you did not explain? Commented Jun 23, 2022 at 12:25
• This sounds like a coordinate transformation problem... in delta space similar to extracting zero rates (Z) dv01 risk from source rates (S) dv01 risk (this is achieved via a Jacobian transformation matrix which is calculated from functions dS/dZ that need to be determined). I think your problem is similar (except in two dimensions) but I'm not quite sure what your second set of instruments would be (there is no zero rate equivalent in swaption vols!) - perhaps a normal vega surface to lognormal vega surface (of different size)? Commented Jun 23, 2022 at 13:17