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Fig. 14.11
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
=
1 with
barrier
B
=
80 and strike
K
=
100
the convergence rate with respect to
ε
at
s
=
100 using various
α
's. As shown in
Fig.
14.9
,therates2
−
α
and 3
−
α
are always obtained.
14.7.3 Barrier Options
Propositions
14.7.3
and
14.7.4
do not hold for barrier options since the option price
is not smooth at the boundary
∂G
. In particular, it is shown in
d
=
1 for tempered
stable densities with 1
<α<
2 and
c
+
=
c
−
that the derivative of the option price
α/
2
−
1
as
x
→
behaves in log-price like
log
B
(see, e.g. [108]). Therefore,
one obtains a large error at the boundary by approximating
X
with
Y
2
.
|
x
−
log
B
|
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