Bank capital regulation in a barrier option framework

Credit Risk Hedging, Deposit Insurance Fund Protection, and Default Risk in Retail Banking during a Financial Crisis

“…Schoenmaker and Gros (2012) suggest that a deposit insurance authority should be established to stabilize the retail deposit base and resolve troubled cross-border banks and the deposit insurance fund would be fed through regular risk-based deposit insurance premiums with a fiscal backstop. Episcopos (2008) demonstrates that raising the regulatory deposit insurance protection leads to a transfer of wealth from the bank's stockholders to the insurer and reduces stockholder incentives to increase asset risk. The primary difference between our model and these papers is that we consider the effects of deposit insurance fund protection with credit risk hedging on bank interest margin and default risk.…”

“…This approach, however, omits a key aspect of the problem of early closure particularly during financial crises. The papers including Bhattacharya et al (1998), Brockman and Turtle (2003), and Episcopos (2008), for example, propose a framework for corporate security based on path-dependent, barrier option models. The fundamental advantage of this approach is also the explicit treatment of uncertainty, in particular early bank closure during a financial turmoil.…”

“…Other examples are Maudos and de Guevara (2004), Williams (2007), Episcopos (2008), Bedendo and Bruno (2012), and Pausch and Welzel (2012). The fundamental insight shared by these papers is that conformity is generated by a design to distinguish oneself from the type with which one wishes not to be identified.…”

“…In general, if the problem of early bank closure is emphasized, then the bank's objective is to maximize its market value based on a path-dependent, barrier option framework. The selection of our model's objective function follows Episcopos (2008). Specifically, we use the barrier option formula of Merton (1973) as a tool to understand the down-and-out call (DOC) option to bank equity in order to address the problem of early closure during a financial turmoil.…”

“…As the barrier increases, debt behaves more like equity and equity converges to zero. Our approach in calculating the value of liabilities is very similar to the one outlined by Episcopos (2008). That is written as:…”