so all good? urgency solved? or?
All fine till now on my side for Spread options. We are are also testing novel PDE methods for spreads.
Of course, we want them for any payoff and any PDE.
And PDE models have the advantage that we do not need (semi-) analytical solutions which can break down for some parameter values. Nice if they exist but a helluva lot of work.
The other scheme can best be described as "Explicit Lithuanian ADE with some western influence (*)" and are even older than Soviet Splitting and the western quant's darling ADI method.
(*) I don't mean John Wayne.