Modeling Banks’ Risk Taking Behavior in a Presence of the Long-Tail Risk Guarantor with the Truncated Version of the St. Petersburg Coin Flip Model

Abstract

This paper draws on the sequential coin toss gamble, used in the St. Petersburg paradox, to model investments with long-tailed risks– those that result in very rare but huge losses. It applies the model to the depository institutions’ assets with long-tail risk, where depositors serve as guarantors of tail risk, and also to other investments with long-tails, such as collateralized debt obligations. The model simulates the financial institutions risk taking behavior, where agents with limited liability are able to shift their tail risk onto external parties who have either imperfect information or act with disaster myopia (i.e. “too big to fail” scenario). A simulation shows that such self-interested agents benefit by increasing leverage and increasing the chance of bankruptcy.