Managing Credit Risk with Credit Derivatives

Given a commercial banking firm facing credit risk we develop a dynamic hedging model where the bank management can use credit derivatives. In a continuous-time framework optimal hedging strategies, deposit and loan decisions and consumption are studied. It is shown that the optimal hedge ratio consists of two elements: a speculative term which is controlled by the risk premium and the bank's risk aversion; and a pure hedge term which depends on the preferences of bank owners. Primarily the purpose of hedging is to stabilize the consumption path through a reduction in the variability of the dynamics of the wealth accumulation. Furthermore, we demonstrate that the asset/liability management is optimal if marginal cost equal marginal revenue for loans and deposits at each instant.