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Fig. 14.12
Relative error for
various values of
ε
using
Y
2
(
14.34
) in place of
X
in (
14.29
) for a barrier option
(
top
) and a non-barrier basket
option (
bottom
)in
d
=
2 with
barrier
B
=
80 and strike
K
=
100
Example 14.7.7
Let
d
=
1 and
d
=
2. We consider again a pure jump process
(
Q
≡
0
)
with one or two (independent) marginal densities of tempered stable type,
i.e.
e
−
β
−
|
z
|
|
e
−
β
−
|
z
|
|
k
i
(z)
=
c
i
1
{
z>
0
}
+
c
i
1
{
z<
0
}
,i
=
1
,...,d .
1
+
α
i
1
+
α
i
z
|
z
|
d
i
=
1
s
i
)
+
1
We compute the price of a down-and-out basket option,
g(s)
=
(K
−
,
)
d
on the domain
D
=[
B,
∞
with barrier
B
=
80, maturity
T
=
0
.
5, strike
K
=
100
1,
β
1
10,
β
1
15,
β
2
9,
β
2
and interest rate
r
=
0
.
01. We set
c
1
=
c
2
=
=
=
=
=
16,
α
1
=
0
.
5 and
α
2
=
=
0
.
7. The option price is shown in Fig.
14.10
where for
d
1
we additionally plot the price for
α
=
1
,
1
.
2 to show the behavior of the option price
close to the barrier.
The relative error for approximating
X
by
Y
2
is plotted in Figs.
14.11
and
14.12
.
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