No-arbitrage pricing under cross-ownership

Details No-arbitrage pricing under cross-ownership No-arbitrage pricing under cross-ownership

2010-05-05

arxiv.org/abs/1005.0768v1

Economy

Quantitative Finance

Pricing of Securities

Excerpts and ideas from this paper have been presented at the Scientific Conference of the German Association for Actuarial an

Scientific paper

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. A result on capital structure irrelevance for groups of firms regarding externally held claims is discussed, as well as financial leverage and systemic risk caused by cross-ownership.

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