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I would like some insight as to how to value modified rainbow options on multiple assets:

For example: A multi asset option, Call GOOG with $S_t$ \$1600 that you may exercise if and only if you also exercise a put on TSLA with $S_t$ \$600 and a call on the SPY with $S_t$ \$400, I have read Jan Stuller's answer to a similar question, but not exactly sure how to generalize this for the option structure above on $n$ securities.

As well, how would a pricing model for a option such as the one above model changes in the correlations of the underlying securities and their volatilities? How would one define the Greeks for an option like this one?

Kareem Sayed
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For more than two underlyings, look here.

It is not a traditional basket option, just external barriers. Usually modelled with Monte Carlo (and a model of choice, or whatever is available). Ideally, SLV.

Greeks will be bump and reprice. In terms of the shape of greeks, this is difficult to answer as there is a number of factors affecting this. You can find simple and intuitive charts here.

AKdemy
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