Risk analytics in financial networks

Abstract

This thesis addresses theoretical, computational, and practical issues on the risk management in financial networks. Based on the celebrated Eisenberg-Noe network model, we focus on three significant questions on this topic which have not been answered at all in the literature: the analysis of firm-specific default probabilities, the computation of systemic risk measures, and the stress testing of financial systems.

The first part of this dissertation aims to explore firm-specific default probabilities in financial networks, focusing on random shocks to financial institutions. Using duality, we characterize the shock amplification caused by the network structure and find the condition when a specific bank fails. Based on such observation, we obtain asymptotic behaviors of firm-specific default probabilities under some distributional assumptions and their simple bounds independent of distributions. More importantly, we provide robust bounds of such probabilities when financial networks are not fully observed.

In the second part, we consider the problem of estimating systemic risk measures including firm-specific default probabilities discussed in the first part. This problem can be generalized as computing expectations over the union of half-spaces. Such a problem also arises in other applications such as option pricing and stochastic activity networks. Assuming that random variables follow a multivariate elliptical distribution, we develop a conditional Monte Carlo method and prove its asymptotic efficiencies. We then demonstrate the numerical performance of the proposed method in three different application areas.

The third and final problem involves the stress testing of Korean financial system. We take an empirical approach based on the data from the Bank of Korea and the Financial Supervisory Service of Korea. In particular, we construct several stress scenarios classified by financial sectors and asset classes, and for each stress scenario, we find the systemic loss and the number of defaults in the system. Furthermore, for each scenario and for each given budget, we address two methods to minimize systemic risk via cash injection conducted by financial regulators and observe how much systemic risk is reduced by applying the new methods.