December 2013
Intermediate to advanced
484 pages
14h 54m
English
Content preview from Nonlinear Option Pricing
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330 Calibration of Local Correlation Models to Market Smiles
situation, ρ
(0,1)
= ρ
∗
is, among all the admissible correlations ρ(t, S
1
, S
2
), the
one with the smallest image. This means that if ρ
(0,1)
= ρ
∗
is not admissible,
then no correlation ρ(t, S
1
, S
2
) is admissible; ρ
(0,1)
t,
S
1
t
S
2
t
= ρ
∗
t,
S
1
t
S
2
t
> 1
corresponds to the situation where
|σ
1
(t) − σ
2
(t)| > σ
12
t,
S
1
t
S
2
t
and ρ
(0,1)
t,
S
1
t
S
2
t
= ρ
∗
t,
S
1
t
S
2
t
< −1 corresponds to the situation where
σ
1
(t) + σ
2
(t) < σ
12
t,
S
1
t
S
2
t
Equation (12.12) tells us that in the case where S
1
and S
2
have no skew, all
admissible correlations have same average value under Q
f
over each line where
S
1
/S
2
is constant, and this common
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