Inference for large financial systems

We treat the parameter estimation problem for mean-field models of large interacting financial systems such as the banking system and a pool of assets held by an institution or backing a security. We develop an asymptotic inference approach that addresses the scale and complexity of such systems. Harnessing the weak convergence results developed for mean-field financial systems in the literature, we construct an approximate likelihood for large systems. The approximate likelihood has a conditionally Gaussian structure, enabling us to design an efficient numerical method for its evaluation. We provide a representation of the corresponding approximate estimator in terms of a weighted least-squares estimator, and use it to analyze the large-system and large-sample behavior of the estimator. Numerical results for a mean-field model of systemic financial risk highlight the efficiency and accuracy of our estimator.