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Cross-Ownership as a Structural Explanation for Over- and Underestimation of Default Probability

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  • Sabine Karl
  • Tom Fischer
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    Abstract

    Based on the work of Suzuki (2002), we consider a generalization of Merton's asset valuation approach (Merton, 1974) in which two firms are linked by cross-ownership of equity and liabilities. Suzuki's results then provide no arbitrage prices of firm values, which are derivatives of exogenous asset values. In contrast to the Merton model, the assumption of lognormally distributed assets does not result in lognormally distributed firm values, which also affects the corresponding probabilities of default. In a simulation study we see that, depending on the type of cross-ownership, the lognormal model can lead to both, over- and underestimation of the actual probability of default of a firm under cross-ownership. In the limit, i.e. if the levels of cross-ownership tend to their maximum possible value, these findings can be shown theoretically as well. Furthermore, we consider the default probability of a firm in general, i.e. without a distributional assumption, and show that the lognormal model is often able to yield only a limited range of probabilities of default, while the actual probabilities may take any value between 0 and 1.

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    File URL: http://arxiv.org/pdf/1301.6069
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1301.6069.

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    Date of creation: Jan 2013
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    Handle: RePEc:arx:papers:1301.6069

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    1. Larry Eisenberg & Thomas H. Noe, 2001. "Systemic Risk in Financial Systems," Management Science, INFORMS, vol. 47(2), pages 236-249, February.
    2. Duffie, Darrell & Huang, Ming, 1996. " Swap Rates and Credit Quality," Journal of Finance, American Finance Association, vol. 51(3), pages 921-49, July.
    3. Zhou, Chunsheng, 2001. "An Analysis of Default Correlations and Multiple Defaults," Review of Financial Studies, Society for Financial Studies, vol. 14(2), pages 555-76.
    4. Helmut Elsinger, 2009. "Financial Networks, Cross Holdings, and Limited Liability," Working Papers 156, Oesterreichische Nationalbank (Austrian Central Bank).
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