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Optimal risk capital under the consideration of systemic risk

In this article, we discuss the determination of the optimal capital level to be increased under the consideration of systemic risk. We establish several models for calculating optimal capital level to be increased in different conditions including without constraint, with constraints of the value of systemic risk ( SVaR ) and the value of expected shortfall of systemic risk ( STVaR ) respectively. We also carry out some numerical analysis with the data from 61 main banks of U.S. and Canada. The risk-based capital in general solvency frameworks do not appropriately account for the interdependencies between assets and liabilities of all financial institutions participating in. And the criterion of risk-based capital is determined based on the insolvency risk of each institution. The recent financial crisis has focused widespread attention on systemic risk in global financial system. Several papers approached how to measure the systemic risk. The representative ones are Acharya, Pedersen, Philippon and Richardsons’(2010),Gauthier, Lehar and Souissi 2010) and Bluhm and Krahnen (2011). Acharya, Pedersen, Philippon and Richardsons’(2010) presented a simple model of systemic risk and they show that the expected shortfall can be used to measure the system risk of whole system and they also propose to use system expected shortfall ( SES ) to measure the contribution of each bank to system risk.