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