We generalize Merton's asset valuation approach to systems of multiple
financial firms where cross-ownership of equities and liabilities is present.
The liabilities, which may include debts and derivatives, can be of differing
seniority. We derive equations for the prices of equities and recovery claims
under no-arbitrage. An existence result and a uniqueness result are proven.
Examples and an algorithm for the simultaneous calculation of all no-arbitrage
prices are provided.