Systemic Risk and Cyclical Economic Environment

Abstract

In this paper, the measurement of systemic risk of financial institutions and the determination of optimal capital level under consideration of systemic risk are discussed. The values of assets and liabilities of financial institutions are considered to be correlated with each other and they are described using Multi-Vasicek Model and are transferred into Gauss process with time varying correlation. The formulas of calculating time varying correlation coefficient are deducted and three advantages of it contrasting to Achayra et al. (2012) are discussed. Default put option pricing model based on Mult-Vasicek Model is first presented to evaluate the expected loss of financial crisis. Four different objective functions are established. They are (1) minimizing the sum of weighted averages of capital cost and expected total loss of financial crisis; (2) minimizing weighted systemically risk value; (3) minimizing weighted systemically expected shortfall and (4) systemically aggregated expected shortfall is at (1- ) confidential level. Optimal solutions can be obtained by solving objective functions. Finally, An application and numerical analysis are carried out by using historical data from the main financial institutions of U.S. and Canada.

Keywords: Systemic Risk; Multi-Vasicek Model; Time Varying Correlation; Gauss Process; Optimal Capital and Weights