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Fig. 16.3
Condition numbers
for different levels and
choices of
k
we choose the CMGY parametrization with state-dependent parameter
Y
given by
Y(x)
0
.
8
e
−
x
2
=
+
0
.
1 in Example
16.6.1
. For the Lévy models we choose constant
1,
β
+
=
β
−
=
Y
∈{
0
.
1
,
0
.
5
,
0
.
7
,
0
.
8
,
0
.
9
}
. In all cases we set
C
=
10 and use trun-
cation parameters
a
3 in log-moneyness coordinates. The prices in the
Feller model are significantly different from the prices in the different Lévy mod-
els. This can be explained by the ability of the Feller model to account for different
tail behavior for different states of the process, which is not possible using Lévy
processes. Figure
16.5
shows the prices of American put option for a Feller process
and for several Lévy models. To enforce the constraint, we use a Lagrangian multi-
plier approach as described in [92, 93], see Chap. 5. The parameters were chosen as
above.
=−
3,
b
=
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