Think of
being an approximation to a hut function (put straddle). The
is calculated in the section
(
Decomposition
of payoff function in one dimension
). We place a lot of high level
wavelets around the singularity at the strike. When we evolve
with Backward Kolmogorov's equation, the singularity disappears. Therefore,
the weights
placed on high order wavelets around the strike should redistribute to lower
order wavelets.
We
produce
by taking
with maximal weights
.
Those
,
not included in
,
would have a small weight
if included in the sum. When we apply the transformation
,
the weights redistribute. The
function
gives us partial information about such redistribution.
We form the
set
We form the set
recursively via distinct
unions
The optimal function
have to depend on diffusive properties of operator
.
However, due to iterative nature of this
procedure,
would work too. In addition, we add propagation into higher scales as follows:
We denote the construction of
from
as
We
calculate
Then we
calculate
We
continue
for
We stop when
becomes small.
After completion, the final set
is reduced by removing indexes with lowest contribution. The result is
.
Another possibility is simply to take
to be a large number and do one iteration.
