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Topics in Statistical Simulation pp 333–341Cite as

Simulating from the Copula that Generates the Maximal Probability for a Joint Default Under Given (Inhomogeneous) Marginals

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Abstract

Starting from two default times with given univariate distribution functions, the copula which maximizes the probability of a joint default can be computed in closed form. This result can be retrieved from Markov-chain theory, where it is known under the terminology “maximal coupling”, but typically formulated without copulas. For inhomogeneous marginals the solution is not represented by the comonotonicity copula, opposed to a common modeling (mal-)practice in the financial industry. Moreover, a stochastic model that respects the marginal laws and attains the upper-bound copula for joint defaults can be inferred from the maximal-coupling construction. We formulate and illustrate this result in the context of copula theory and motivate its importance for portfolio-credit risk modeling. Moreover, we present a sampling strategy for the “maximal-coupling copula”.

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Notes

  1. 1.

    In the terminology of F. Knight one might say that one is exposed to uncertainty concerning the dependence structure.

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Acknowledgements

The authors would like to thank Alfred Müller and an anonymous referee for valuable remarks.

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Authors and Affiliations

  1. XAIA Investment GmbH, Sonnenstraße 19, 80331, München, Germany

    Jan-Frederik Mai

  2. Technische Universität München, Parkring 11, 85748, Garching-Hochbrück, Germany

    Matthias Scherer

Authors
  1. Jan-Frederik Mai
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  2. Matthias Scherer
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Corresponding author

Correspondence to Matthias Scherer .

Editor information

Editors and Affiliations

  1. St.Petersburg State University, St.Petersburg, Russia

    V.B. Melas

  2. University of Bologna, Rimini, Italy

    Stefania Mignani

  3. University of Bologna, Rimini, Italy

    Paola Monari

  4. University of Padova, Padova, Italy

    Luigi Salmaso

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Mai, JF., Scherer, M. (2014). Simulating from the Copula that Generates the Maximal Probability for a Joint Default Under Given (Inhomogeneous) Marginals. In: Melas, V., Mignani, S., Monari, P., Salmaso, L. (eds) Topics in Statistical Simulation. Springer Proceedings in Mathematics & Statistics, vol 114. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2104-1_32

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