Many financial systems are effectively described by temporal networks whose evolution describes the dynamics of interaction between the constituent parts. Due to the high dimensionality of the system, the potential presence of non-stationarities, and, in general, the effect of exogenous variables on network topology, the modeling is particularly challenging. In this talk, Fabrizio Lillo will present some advancements in this topic starting from the well-known framework of Exponential Random Graph Models (or max-entropy ensembles). In particular, he will focus on (i) how to characterize and predict the response of a temporal network to a shock and (ii) how to model a non-stationary temporal network and its dependence on external covariates. They present an empirical application to the electronic Market of Interbank Deposit (e-MID) network with a focus on the turmoil period of the European sovereign debt crisis.