An Option Approach of Valuing Banks' Debts under the Volcker Rule

Financial regulators are increasingly taking aim at the culture of Wall Street by demanding risk mitigation. Proprietary trading with its accompanying lucrative and yet risky operations was one of the key drivers of the 2008 financial crisis. Several banks traded for their own gains at extremely high risks so much so that banks such as Goldman Sachs and Morgan Stanley wrote off billions of dollars they lost in commercial real estate funds. These forfeitures were the propelling factors behind the adoption of the Dodd-Frank rules of which the Volcker Rule has become the center. Extending on Geske’s approach, we show that the pattern of default probabilities is a function of the liability structure of the financial institution. The assumptions made by our framework on capital structure change when liabilities come due. We demonstrate that in the context of the Volcker rule, the variations of the default risks are crucial in measuring and managing default risks in banks. Our model thus attests that the periodic default probability is highest in the initial period. In practice, it means that the largest threat to the survival of a financial firm is in the short term. This utterly justifies the Volcker rule. As the default probability rises, the near term default becomes the driving force. Henceforth, the Volcker rule becomes very relevant in that it prevents the banks from defaulting when the short-term default risk is unusually high. Ultimately, the model shows that in times of financial crisis when the short-term default risk is very high, a large level of capital infusion is required to increase survival probability