# Term for a class of multi-asset options that determine the joint distribution of a set of assets?

For a single asset we can infer (in theory) the exact distribution of future outcomes via option prices: Either via option butterflies or the Breeden-Litzenberger formula.

Is there a name for (one of) the classes of multi-options that determine (i.e. can be used to compute) the joint distribution of several assets?

For two assets $$X,Y$$, for example, "pair-options" with payoff of the form $$\mathbf 1\{X\geq K_1\}(Y-K_2)^+,$$ with $$K_1,K_2\in\mathbb R$$ and the roles of $$X,Y$$ switched, should be one such family. This is because it allows us to construct butterflies for (and hence get the distribution of) $$Y$$, conditional on $$X\geq K_1$$, etc.

(Is there a publicly available historical dataset consisting of "pair-options" or suitable alternatives as above?)