volatility trade

[Perissin Francesco]

Hi all,
I need to build a structure with the following constrains:
- I have to use only vanilla options and cash (same underlying, whatever...)
- I want to have a risk profile which is essentially long vega and with as low delta - gamma as possible.
- the overall structure should be capital-guaranteed (i.e. I cannot sell options "uncovered")

I know that there should be some articles about this issue, but I cannot find any...

is there anybody who know something about?

Thanks
Francesco

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[Ferdinando Ametrano-3]

Hi Francesco

> I need to build a structure with the following constrains:
> - I have to use only vanilla options and cash (same underlying,
> whatever...)
> - I want to have a risk profile which is essentially long vega and with
> as low delta - gamma as possible.
> - the overall structure should be capital-guaranteed (i.e. I cannot sell
> options "uncovered")

I would consider buying a zero coupon maturing at time T for the
capital-guaranteed requirement, and invest the remaining capital in a
variance swap contract replicated with vanilla options (it's a
model-independent replication). A variance swap is a forward contract on
the realized variance of a given underlying, with no delta/gamma
exposure. You would have a residual delta/gamma risk due to the
approximation of your replication strategy.

> I know that there should be some articles about this issue, but I cannot
> find any...
start with "More Than You Ever Wanted To Know About Volatility Swaps",
by Demeterfi, Derman, Kamal, and Zou
(http://www.ederman.com/emanuelderman/GSQSpapers/volswaps.pdf), then
consider:
http://www.chicagofed.org/publications/capitalmarketnews/2001/cmn200101.pdf
http://volatility.martinsewell.com/ChMo99.pdf
http://www.math.nyu.edu/fellows_fin_math/gatheral/Lecture6_Fall2002.pdf

and related references.

Beware I'm suggesting a variance swap, not a volatility swap. A vol swap
  is a completely different beast, which cannot be replicated using
vanilla options.

hope it helps

ciao -- Nando