December 2015
Intermediate to advanced
522 pages
20h
English
Content preview from Stochastic Volatility Modeling
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Forward-start options 123
Figure 3.2
:
dbσ
T
d ln S
0
/
dbσ
F
T
T
d ln S
0
ratio in the local volatility model, as a function of maturity
– in years – for the Euro Stoxx 50 index smiles of October 4, 2010 (left) and May 16,
2013 (right).
already mentioned that, because of the steepness of market smiles, unless one takes
into account – at least at order one – the correction to the density in equation (2.32),
the approximation is inaccurate.
This issue is magnied in the case of the log contract: for vanilla options, the
dollar gamma restricts integration in (2.32) to a region of spot prices around
K
, thus
reducing the dependence of implied volatilities of vanilla options ...
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