A model-free approach to delta hedging



1200


1000


7000

6500

6000

5500

5000

4500

4000

3500

3000

2500

2000



0          500         1000        1500        2000        2500


(a) Underlying asset: daily values of the CAC from

28 April 2000 until 18 September 2009


3000


inria-00457222, version 1 - 16 Feb 2010


800


600


400


200


Il '       ” All

W '  ....... λ∕⅜

It I '     l5" Æ M

s.               ⅛ ....... '            А


0         200        400        600        800        1000       1200


0         200        400        600        800        1000       1200


(b) Option: CFU9PY3500 daily prices from 9 May (c) Option: CFU9CY3500 daily prices from 9 May


2009 until 18 September 2009


2009 until 18 September 2009


Figure 1: Daily data


4 Conclusion

Lack of space prevented us from examining more involved options, futures, and
other derivatives, than in Section 2.3. Subsequent works will do that, and also
introduce several time scales thanks to the
nonstandard analytic framework of
the Cartier-Perrin theorem [4].

Acknowledgement. The authors would like to thank Frederic Hatt for stim-
ulating discussions.

References

[1] BechU T., Bertrand E., Nebenzahl J., L’analyse technique (6e ed.),
Economica, 2008.

[2] Bernhard P., El Farouq N., Thiery S., Robust control approach
to option pricing: a representation theorem and fast algorithm,
SIAM J.
Control Optimiz.
, 46, 2280-2302, 2007.




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