I am more of a probabilist than a financial mathematician. I am currently working on the features of American put options under a particular stochastic volatility model.
Like most stochastic volatility models, it is incomplete. (In fact, it would be nice if someone tell me a complete, stochastic volatility model, is there any?) In my current treatment, I have just treated the model as a maths toy. I have chosen an arbitrary risk neutral measure and try to say something about the value of options. (Of course, the proofs holds in any EMM.)
Though the question I asked here is not extremely closely related to what I am doing, I would still like to know:
How does someone choose an EMM? Do you restrict yourself to a subclass of EMM and give yourself some parameters which you try to fit using given data?