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Fig. 9.1
Option price (
top
)
and convergence rate
(
bottom
) for the mean
reverting OU model
b
k
S
w(x
k
)
i
k
,i
k
b
i
k
(x
k
)b
i
k
(x
k
)w(x
k
)
d
x
k
,
:=
a
k
b
k
B
w(x
k
)
b
i
k
(x
k
)b
i
k
(x
k
)w(x
k
)
d
x
k
,
i
k
,i
k
:=
a
k
b
k
M
w(x
k
)
i
k
,i
k
:=
b
i
k
(x
k
)b
i
k
(x
k
)w(x
k
)
d
x
k
,
a
k
where
by
b
i
k
:
(a
k
,b
k
)
→ R
≥
0
we
denote
the
hat-function
b
i
k
(x
k
)
:=
h
−
1
k
max
{
0
,
1
−
|
x
k
−
x
k,i
k
|}
with respect to the
k
th coordinate direction on a
uniform mesh
x
k,i
k
:=
a
k
+
i
k
h
k
,
i
k
=
0
,...,N
k
+
1, with mesh width
h
k
:=
(b
k
−
a
k
)/(N
k
+
1
)
.
We now prove a representation of the stiffness matrix
A
SV
corresponding to the
bilinear form
a
SV
(
·
,
·
)
in (
9.28
).
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