# How to choose a risk-neutral measure when the market is incomplete?

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?

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There won't be a non-degenerate complete stochastic volatility model. An informal way of thinking about it is that the space of randomness is two dimensional (two BM's driving things), and the space of attainable claims is just one-d –  quasi Jan 15 at 23:34
@quasi i see, unless you can trade volatility as an asset, this is starting to ring a bell. –  Lost1 Jan 16 at 0:54