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Ito's Lemma
Ito's Lemma
2 selected
Difficulty 5-6
2 unseen
View topic
Intermediate
New
0 answered
2 intermediate
Adapts to your performance
Question 1 of 2
120s
intermediate (5/10)
compute
Apply Ito's lemma to
f
(
x
)
=
lo
g
x
on geometric Brownian motion
d
S
t
=
μ
S
t
d
t
+
σ
S
t
d
W
t
. What does
d
(
lo
g
S
t
)
equal?
Hide and think first
A.
d
(
lo
g
S
t
)
=
μ
d
t
+
σ
d
W
t
, the deterministic chain rule applied to
lo
g
without an Ito correction
B.
d
(
lo
g
S
t
)
=
(
μ
−
2
1
σ
2
)
d
t
+
σ
d
W
t
, with the
−
2
1
σ
2
Ito correction visible
C.
d
(
lo
g
S
t
)
=
(
μ
+
2
1
σ
2
)
d
t
+
σ
d
W
t
, with the correction *added* to the drift
D.
d
(
lo
g
S
t
)
=
μ
d
t
+
2
1
σ
2
d
W
t
, with the
2
1
σ
2
correction multiplying the noise term
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