We formulate the optimal balance sheet management problem as a linear program and study it using a duality approach. In addition to helping determine the optimal balance sheet, the dual problem also provides us the interest rate risk and credit risk pricing. We deploy our methodology to determine premia on credit risk and interest rate risk for commercial banks, which allows us to manage the risk allocation for a bank given a risk budget. Moreover, our approach will be of interest to regulators, who can use it to assess the price of credit and interest rate risk at each point in the economic cycle. Finally, we apply this methodology to real data and show how it can be used in a real-world setting, using diversification constraints and a greedy algorithm that results in the optimal asset-liability allocation.

We propose a dynamic framework which encompasses the main risks in balance sheets of banks in an integrated fashion. Our contributions are fourfold: (1) solving a simple one-period model that describes the optimal bank policy under credit risk; (2) estimating the long-term stochastic processes underlying the risk factors in the balance sheet, taking into account the credit and interest rate cycles; (3) simulating several scenarios for interest rates and charge-offs; and (4) describing the equations that govern the evolution of the balance sheet in the long run. The models that we use address momentum and the interaction between different rates. Our results enable simulation of bank balance sheets over time given a bank’s lending strategy and provides a basis for an optimization model to determine bank asset–liability management strategy endogenously.