Optimal Regulation of Systemic Risk by Tax

Abstract

Financial systemic crisis could be broadly understood as the deterioration of the banking sector which results in damage to the real economy. From elementary accounting, a firm's financial position can be characterized by the value of its asset holdings versus the amount it borrow from others. If assets are not worth sufficiently more than the firm owes, it will be in distress, and will not be able to operate its business efficiently. In the case of a bank, this means the difference between the dollar amount it lends and the amount it receives from depositors is not sufficiently high or even worse, is negative. If either case happens to the aggregate banking sector, a systemic crisis will ensue, and there will be significant costs incurred by society. This M.Sc. thesis will concentrate on an existing economic model which incorporates the risk of systemic crisis, as defined above, at a future time. In the context of this model, a tax as a function of the banks' dollar value of investments, raised debt, and equity funding at present time will incentivize them to choose these quantities in the interest of social welfare. The thesis will provide mathematical explanations for this effect. Moreover, MATLAB codes are included to calculate the tax amounts charged to each bank when they behave in a socially optimal manner.