December 2015
Intermediate to advanced
522 pages
20h
English
Content preview from Stochastic Volatility Modeling
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16 Stochastic volatility modeling
We must thus choose
bσ = bσ
O
. We now have for
P
a pricing function that
explicitly depends on two dynamical variables: S and bσ
O
:
P (t, S, bσ
O
)
which is natural as we are using two instruments as hedges.
This is an elementary instance of calibration: we decide to make our exotic
option’s price a function of other derivatives’ prices. It is a trading decision.
In the unhedged case we were free to chose the implied volatility
bσ
as our best
estimate of future realized volatility and kept it constant throughout: no P&L was
generated by the variation of bσ.
Unlike
bσ
, however,
bσ
O
is a market implied volatility and cannot be kept ...
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