Message-ID: <21650103.1075856539864.JavaMail.evans@thyme>
Date: Tue, 7 Nov 2000 09:43:00 -0800 (PST)
From: vince.kaminski@enron.com
To: vkaminski@aol.com
Subject: Contstraints on the shape of a smile
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---------------------- Forwarded by Vince J Kaminski/HOU/ECT on 11/07/2000 
05:40 PM ---------------------------
   
	Enron Capital & Trade Resources Corp. - Europe
	
	From:  Sharad Agnihotri                           11/07/2000 04:22 PM
	

To: Stinson Gibner/HOU/ECT@ECT, Zimin Lu/HOU/ECT@ECT, Vince J 
Kaminski/HOU/ECT@ECT
cc: Steven Leppard/LON/ECT@ECT 
Subject: Contstraints on the shape of a smile

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