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?
Answer
Hum, that's one of the most important questions in financial engineering, that why no answer is proposed.
If you have available data as option prices, you may calibrate a parametric EMM but nothing can tell that it's the best EMM (cause there is no best EMM).
So make a choice and defend your choice by saying 'it's simple and allows beautiful result' like every body use to do.
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