Interpolation of shift values for shifted EUR swaption vol?

marlar01 · April 27th, 2016, 5:25 pm

Hi, take ICAP VCAP1A (Shifted black ATM swaption vols) in EUR as example (with the shift values per underlying maturity in VCAP1B), if 10Y shift is 1,52% and 15Y (next value) is 1,50%. If I want to price say a 12Y underlying, what shift value would I use? 1,52 ("flat extrapolation") or ~1,51% ("linear interpolation)? Flat extrapolation before 1Y (first point) and beyond 30Y (last point)? Thank you.

overkill112358 · April 27th, 2016, 7:43 pm

I'd use linear interpolation in shift or convert into equivalent normal vols in the first place and interpolate those. I think ICAP must be showing normal vols as well when it shows shifted lognormal ones.

doublebarrier2000 · May 2nd, 2016, 5:18 pm

generally use the same interpolation for the shift as for the standard parameters

marlar01 · May 3rd, 2016, 6:17 am

Ok, not sure what "standard parameters" would be for a simple Displaced Black ATM swaption surface (for simple case vol interpolation I typically use Linear though in Expiry/Strike/UnderlyingMaturity). Linear in the quoted Shift Values sound sensible I guess (else maybe discontinuities in pricing once you go from one shift size to the other) (and Flat extrapolation for the unlikely case of UndMat<1Y or >30Y I assume). Conversion via black normal vols seems a bit overkill for my usage (if no one says this is "a convention"..). Thank you for input.