Message-ID: <30681369.1075856596070.JavaMail.evans@thyme>
Date: Tue, 7 Nov 2000 14:22:00 -0800 (PST)
From: sharad.agnihotri@enron.com
To: stinson.gibner@enron.com, zimin.lu@enron.com, vince.kaminski@enron.com
Subject: Contstraints on the shape of a smile
Cc: steven.leppard@enron.com
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Stinson ,Vince ,Zimin,

Here's a brief document on constraints on the shape of a smile for a fixed 
expiry date.
the constraints are neccessary and sufficient for no arbitrage in this case.
I've used a template created by Dr. Leppard which is why it looks so scary. 

If you need constraints in the time direction then I will have to think a 
little bit more about it.
I think constraints in this direction are very model depenendent e.g. 
stochastic volatility and local volatility models
will throw up different constraints.





Steve,
I am not sure if our traders (or quants for that matter) are aware of these 
constraints
and some desks are beginning to build smiles...

Regards
Sharad