Survey_BK_2011

Abstract

The model which is set up in this section captures important features of the nancial system and replicates several stylized facts encountered during the recent nancial crisis. It consists of (i) a system of three interconnected nancial institutions that adjust their portfolio to ful ll a capital requirement and (ii) the Rest of the World (ROW). Banks have deposits, lend to each other, and hold liquid assets (LA) and non-liquid assets (NLA) on their balance sheet. Non-liquid assets are marked to market11 while liquid assets do not change their value on banks' balance sheets. Shocks in the model come in the form of percentage loss in asset values. The resulting systemic risk is calculated as the ratio of assets from defaulting banks to system-wide asset total, both measured prior to the shock. Our modeling strategy allows to adopt the Value at Risk (VaR) metros,16 the standard risk management tool used in microprudential supervision, for a macroprudential problem. The resulting metric, the System Value-at-Risk (SVaR), is e ectively a set of stress tests for an entire banking system. This metric, expected systemic risk, will be used subsequently to analyze systemic risk in the nancial system. To identify the contribution of an individual bank to expected systemic risk, the Shapley value methodology can be employed. In game theory this value is used to nd the fair allocation of gains obtained by cooperation among players. To minimize the loss-function outlined in Section 5 (Equation (14)) the simulated annealing algorithm is used. The algorithm has been developed by Kirkpatrick, Gelatt, and Vecchi (1983) and is a heuristic optimization procedure to approximate the global minimum of a complex function that has multiple local minima.46 It has been inspired from the annealing process in metallurgy where a slow cooling down of metal insures that atoms have enough time to form stable crystals without defects. To minimize a function with the simulated annealing algorithm, new function values are generated along random changes to the control parameters in a Markov chain. New solutions that lead to improvements, that is, decreasing values, in the function are always accepted as new element in the Markov chain, whereas new solutions that lead to an increase in the function value are only accepted with a certain probability. This acceptance probability is in uenced by a temperature used in the algorithm.