Financial networks help firms manage risk but also enable financial shocks to spread. Despite their importance, existing models of financial networks have several limitations. Prior works often consider a static network with a simple structure (e.g., a ring) or a model that assumes conditional independence between edges. We propose a new model where the network emerges from interactions between heterogeneous utility-maximizing firms. Edges correspond to contract agreements between pairs of firms, with the contract size being the edge weight. We show that, almost always, there is a unique "stable network." All edge weights in this stable network depend on all firms' beliefs. Furthermore, firms can find the stable network via iterative pairwise negotiations. When beliefs change, the stable network changes. We show that under realistic settings, a regulator cannot pin down the changed beliefs that caused the network changes. Also, each firm can use its view of the network to inform its beliefs. For instance, it can detect outlier firms whose beliefs deviate from their peers. But it cannot identify the deviant belief: increased risk-seeking is indistinguishable from increased expected profits. Seemingly minor news may settle the dilemma, triggering significant changes in the network.