he interval
was inserted into the problem (
Example Black
problem
) to avoid considering a PDE problem on the entire real line. We
constructed a basis of functions with finite support, unsuitable for finite
element calculation on unbounded set. We would like to place the numbers
to positions according to the
rule
for some number
.
The process
is given by the
SDE
We
calculate
The distribution density
of
is a symmetric function
Thus, we take
as a controlling
parameter:
for a fixed positive number
.
The only remaining step is to make sure that the interval
is adapted to binary structure of wavelet basis. We choose a scale parameter
then
The parameter
should be taken so
that
would be comparable to precision of initial approximation of the payoff
function, discussed in the section
(Decomposition
of payoff function in one dimension
). The parameter
should be taken to be the minimal number needed to provide the condition
(
Sufficiently fine scale 2
).
