For example, weather derivatives market. Is it like pricing an insurance in this case?

In an incomplete market there is no such thing as risk-neutral pricing. The best you can do is use real-world models (e.g. actuarial tools might be used to model prepayment risk in mortgages). This allows you to construct a real-world distribution for the option value. You could then take the mean and add a number of standard deviations to give a conservative price, and then discount it of course. Once you have this model in place, you could put together a hedge simulation and see what your terminal P&L looks like.

the problem is that the EMM is not unique, or equivalently the price of risk is not uniquely determined. i am not from industry, so i could only provide the idea from academic point of view as follows:set up a general equilibrium model with representative agent who has a risk-aversed utilitiy function. the optimal trading strategy of the agent pins down the particular price of risk, i.e. the unique risk neutral measure, under which all traded assets are priced.btw, björk's book has a chapter about pricing in incomplete market that can help in details.cheers,jin

I'm not familiar with pricing models for weather derivatives, but if someone asked me to give it a go, I would probably just chose some representative dynamics for the underlying calibrated to real meteorological data, add in some seasonality effects. I guess you might want to try to capture freak events, so possibly some jumps. What's the skew look like in weather derivatives? In fact, what are the contracts actually written on? Insurance payouts?

QuoteOriginally posted by: lesliejinyuthe problem is that the EMM is not unique, or equivalently the price of risk is not uniquely determined. i am not from industry, so i could only provide the idea from academic point of view as follows:set up a general equilibrium model with representative agent who has a risk-aversed utilitiy function. the optimal trading strategy of the agent pins down the particular price of risk, i.e. the unique risk neutral measure, under which all traded assets are priced.btw, björk's book has a chapter about pricing in incomplete market that can help in details.cheers,jinBjork definitely overuses the word "exongenously", but otherwise is a pleasant read. Here is free stuffClick on Lecture 6.