How do capital structure and economic regime affect fair prices of bank’s equity and liabilities?

This paper considers the capital structure of a bank in a continuous-time regime-switching economy. The modeling framework takes into account various categories of instruments, including equity, contingent convertible debts, straight debts, deposits and deposits insurance. Whereas previous researches concentrate on the determination of the capital structure that maximizes shareholders’ equity, this work focuses on the fair pricing of liabilities that ensures no cross-subsidization among stakeholders. This is discussed in a case study where the bank’s EBIT is modeled by a four-regime process and is fitted to real market data. A numerical analysis reveals that convertible debts can significantly reduce the cost of deposits insurance and straight debts as well as probabilities of bankruptcy. Although it is found that the risk of dilution for shareholders is important, paradoxically, a high conversion rate for the contingent convertible debt, compensated by a low interest cost before conversion, can delay this dilution. Finally, we find that in case of change of economic regime, there exists an optimal capital structure from the shareholder’s perspective.