Posted by
Ferdinando Ametrano-3 on
Jul 21, 2004; 1:57am
URL: http://quantlib.414.s1.nabble.com/volatility-trade-tp3072p3073.html
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.pdfhttp://volatility.martinsewell.com/ChMo99.pdfhttp://www.math.nyu.edu/fellows_fin_math/gatheral/Lecture6_Fall2002.pdfand 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