Liquidation equilibrium with seniority and hidden CDO

The aim of our paper is to price credit derivatives written on a single name when this name is a bank. Indeed, due to the special structure of the balance sheet of a bank and to the interconnections with other institutions of the financial system, the standard pricing formulas do not apply and their use can imply severe mispricing. The pricing of credit derivatives written on a single bank name requires a joint analysis of the risks of all banks directly or indirectly interconnected with the bank of interest. Each name cannot be priced in isolation, but the banking system must be treated as a whole. It is necessary to analyze the contagion of losses among banks, especially the equilibrium of joint defaults and recovery rates at liquidation time. We show the existence and uniqueness of such an equilibrium. Then the standard pricing formulas are modified by adding a premium to capture the contagion effects.