Systemic risk in a mean-field model of interbank lending with self-exciting shocks

In this paper we consider a mean-field model of interacting diffusions for the monetary reserves in which the reserves are subjected to a self- and cross-exciting shock. This is motivated by the financial acceleration and fire sales observed in the market. We derive a mean-field limit using a weak convergence analysis and find an explicit measure-valued process associated with a large interbanking system. We define systemic risk indicators and derive, using the limiting process, several law of large numbers results and verify these numerically. We conclude that self-exciting shocks increase the systemic risk in the network and their presence in interbank networks should not be ignored

Systemic risk in a mean-field model of interbank lending with self-exciting shocks

In this paper we consider a mean-field model of interacting diffusions for the monetary reserves in which the reserves are subjected to a self- and cross-exciting shock. This is motivated by the financial acceleration and fire sales observed in the market. We derive a mean-field limit using a weak convergence analysis and find an explicit measure-valued process associated with a large interbanking system. We define systemic risk indicators and derive, using the limiting process, several law of large numbers results and verify these numerically. We conclude that self-exciting shocks increase the systemic risk in the network and their presence in interbank networks should not be ignored

Developing a Framework to Assess Financial Stability: Conference Highlights and Lessons

Central banks are still defining their approach to financial stability and are at an early stage in the development of useful models. The Bank of Canada's 2007 economic conference was organized to stimulate progress in the development of financial-stability frameworks. Among the highlights reported here are the discussions centred around three proposed frameworks: a contingent-claims-analysis framework, a semi-structural framework, and structural financial-stability models. Participants also reported on their experiences with stress-testing under the International Monetary Fund's Financial Sector Assessment Program and discussed the implications for financial stability of linkages among payment, clearing, and settlement systems.

Modelling bonds and credit default swaps using a structural model with contagion

This paper develops a two-dimensional structural framework for valuing credit default swaps and corporate bonds in the presence of default contagion. Modelling the values of related firms as correlated geometric Brownian motions with exponential default barriers, analytical formulae are obtained for both credit default swap spreads and corporate bond yields. The credit dependence structure is influenced by both a longer-term correlation structure as well as by the possibility of default contagion. In this way, the model is able to generate a diverse range of shapes for the term structure of credit spreads using realistic values for input parameters