December 2015
Intermediate to advanced
522 pages
20h
English
Content preview from Stochastic Volatility Modeling
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Forward variance models 237
over any nite interval
[t, t
0
]
as, from (7.42), the P&L of such a position is simply
P &L = (U
t
0
− U
t
).
The conclusion is that, while
Q
t
itself is not hedgeable, the package consisting of
Q
t
+(T − t) bσ
2
T
(t)
can be exactly replicated:
U
t
is a legitimate underlying. Moreover
the pricing drift of
U
is zero, since taking a VS position involves no cash outlay. This
is consistent with the expression of U in terms of forward variances:
U
t
=
1
T
Z
t
0
ξ
τ
τ
dτ +
Z
T
t
ξ
τ
t
dτ
(7.44)
where the rst piece in the right-hand side of (7.44) corresponds to past observations.
As the
ξ
τ
are driftless, so is
U
. From denition (7.43), the values of
U
at
t = 0
and
t = T
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