Hi! We have a situation where the vols for the ATM swaptions are "known" (market) and users provide the vols for non-ATM swaptions for a series of strikes (specified as spreads over the ATM strike), but not for all NXM swaptions, rather for a limited subset (e.g., 1X1, 2X2, 3X3, ...). I have been looking for references to methods of extrapolating these vols to fill the whole 3D swaption vol cube, without much success. I have found references to robust interpolation/extrapolation based on Voronoi diagrams, which looks very powerful but perhaps a little bit of overkill, as the data is more or less structured (i.e., all ATM vols, all vols for non-ATM swaptions of some specified expiries and terms). I would appreciate any comments on this topic. Thanks!

Hi Francisco,This problem is well known when doing adaptive computations when you havethe need to interpolate data from one "mesh" to another. I your case, you have a"structured" mesh and a quadtree search (octree in 3D) will be efficient.You can have a look to the book of Lohner (chapter 13 : Interpolation) wherehe presents different efficient algorithms for interpolation.Farid.