•We propose a new model to reflect effects of risk-based capital rules on volatility.•The regulator imposes dynamic limits on the asset risk of financial institutions.•Volatility is reduced when capital cushion becomes too small (leverage too high).•Regulation reduces cost of deposit insurance, credit spread, and default probability.•Merton (1974), Black and Cox (1976) are special cases of our dynamic volatility model. Unlike non-financial firms, financial institutions are often heavily regulated to prevent bankruptcies and negative spillovers. A main regulatory tool is risk-based capital requirements. To reflect this reality, we develop a model that allows for dynamically updated asset risk, in contrast to standard contingent claim models that assume constant volatility. Regulators impose a decrease in asset volatility when the capital cushion becomes small, thereby reducing the risk of distress. We show that such regulation of financial institutions affects their credit spreads, credit ratings, transition matrices, valuation of liabilities, cost of deposit insurance, and risk-shifting incentives.