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Efficient solution of structural default models with correlated jumps and mutual obligations

Author

Listed:
  • Andrey Itkin
  • Alexander Lipton
Abstract
The structural default model of Lipton and Sepp, 2009 is generalized for a set of banks with mutual interbank liabilities whose assets are driven by correlated Levy processes with idiosyncratic and common components. The multi-dimensional problem is made tractable via a novel computational method, which generalizes the one-dimensional fractional partial differential equation method of Itkin, 2014 to the two- and three-dimensional cases. This method is unconditionally stable and of the second order of approximation in space and time; in addition, for many popular Levy models it has linear complexity in each dimension. Marginal and joint survival probabilities for two and three banks with mutual liabilities are computed. The effects of mutual liabilities are discussed, and numerical examples are given to illustrate these effects.

Suggested Citation

  • Andrey Itkin & Alexander Lipton, 2014. "Efficient solution of structural default models with correlated jumps and mutual obligations," Papers 1408.6513, arXiv.org, revised Nov 2014.
    • Handle: RePEc:arx:papers:1408.6513
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    References listed on IDEAS

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    3. Andrey Itkin & Peter Carr, 2012. "Using Pseudo-Parabolic and Fractional Equations for Option Pricing in Jump Diffusion Models," Computational Economics, Springer;Society for Computational Economics, vol. 40(1), pages 63-104, June.
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    Cited by:

    1. Vadim Kaushansky & Alexander Lipton & Christoph Reisinger, 2016. "Numerical analysis of an extended structural default model with mutual liabilities and jump risk," Papers 1701.00030, arXiv.org.
    2. Alexander Lipton, 2016. "Modern Monetary Circuit Theory, Stability Of Interconnected Banking Network, And Balance Sheet Optimization For Individual Banks," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(06), pages 1-57, September.
    3. Andrey Itkin, 2017. "Modelling stochastic skew of FX options using SLV models with stochastic spot/vol correlation and correlated jumps," Applied Mathematical Finance, Taylor & Francis Journals, vol. 24(6), pages 485-519, November.
    4. Laura Ballota & Griselda Deelstra & Grégory Rayée, 2015. "Quanto Implied Correlation in a Multi-Lévy Framework," Working Papers ECARES ECARES 2015-36, ULB -- Universite Libre de Bruxelles.
    5. Vadim Kaushansky & Alexander Lipton & Christoph Reisinger, 2017. "Transition probability of Brownian motion in the octant and its application to default modeling," Papers 1801.00362, arXiv.org, revised May 2018.
    6. Alexander Lipton, 2015. "Modern Monetary Circuit Theory, Stability of Interconnected Banking Network, and Balance Sheet Optimization for Individual Banks," Papers 1510.07608, arXiv.org.
    7. Alexander Lipton & Vadim Kaushansky & Christoph Reisinger, 2018. "Semi-analytical solution of a McKean-Vlasov equation with feedback through hitting a boundary," Papers 1808.05311, arXiv.org, revised Aug 2018.
    8. Andrey Itkin & Alexander Lipton, 2017. "Structural default model with mutual obligations," Review of Derivatives Research, Springer, vol. 20(1), pages 15-46, April.
    9. Andrey Itkin, 2015. "LSV models with stochastic interest rates and correlated jumps," Papers 1511.01460, arXiv.org, revised Nov 2016.
    10. Ballotta, Laura & Fusai, Gianluca & Marazzina, Daniele, 2019. "Integrated structural approach to Credit Value Adjustment," European Journal of Operational Research, Elsevier, vol. 272(3), pages 1143-1157.

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