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Structural default model with mutual obligations


  • Andrey Itkin
  • Alexander Lipton


This paper considers mutual obligations in the interconnected bank system and analyzes their influence on joint and marginal survival probabilities as well as CDS and FTD prices for the individual banks. To make the role of mutual obligations more transparent, a simple structural default model with banks' assets driven by correlated multidimensional Brownian motion with drift is considered. This model enables a closed form representation for many quantities of interest, at least in a 2D case, to be obtained, and moreover, model calibration is provided. Finally, we demonstrate that mutual obligations have to be taken into account in order to get correct values for model parameters.

Suggested Citation

  • Andrey Itkin & Alexander Lipton, 2015. "Structural default model with mutual obligations," Papers 1505.02039,
  • Handle: RePEc:arx:papers:1505.02039

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    References listed on IDEAS

    1. Metzler, Adam, 2010. "On the first passage problem for correlated Brownian motion," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 277-284, March.
    2. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-470, May.
    3. Andrey Itkin, 2013. "Efficient Solution of Backward Jump-Diffusion PIDEs with Splitting and Matrix Exponentials," Papers 1304.3159,, revised Apr 2014.
    4. Alexander Lipton & Ioana Savescu, 2014. "Pricing credit default swaps with bilateral value adjustments," Quantitative Finance, Taylor & Francis Journals, vol. 14(1), pages 171-188, January.
    5. Black, Fischer & Cox, John C, 1976. "Valuing Corporate Securities: Some Effects of Bond Indenture Provisions," Journal of Finance, American Finance Association, vol. 31(2), pages 351-367, May.
    6. Christophette Blanchet-Scalliet & Fr'ed'eric Patras, 2008. "Counterparty risk valuation for CDS," Papers 0807.0309,
    7. Andrey Itkin & Alexander Lipton, 2014. "Efficient solution of structural default models with correlated jumps and mutual obligations," Papers 1408.6513,, revised Nov 2014.
    8. Larry Eisenberg & Thomas H. Noe, 2001. "Systemic Risk in Financial Systems," Management Science, INFORMS, vol. 47(2), pages 236-249, February.
    9. Lewis Webber & Matthew Willison, 2011. "Systemic capital requirements," BIS Papers chapters,in: Bank for International Settlements (ed.), Macroprudential regulation and policy, volume 60, pages 44-50 Bank for International Settlements.
    10. Zhou, Chunsheng, 2001. "The term structure of credit spreads with jump risk," Journal of Banking & Finance, Elsevier, vol. 25(11), pages 2015-2040, November.
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    Cited by:

    1. Vadim Kaushansky & Alexander Lipton & Christoph Reisinger, 2017. "Transition probability of Brownian motion in the octant and its application to default modeling," Papers 1801.00362,, revised May 2018.
    2. Vadim Kaushansky & Alexander Lipton & Christoph Reisinger, 2016. "Numerical analysis of an extended structural default model with mutual liabilities and jump risk," Papers 1701.00030,
    3. Alexander Lipton & Vadim Kaushansky & Christoph Reisinger, 2018. "Semi-analytical solution of a McKean-Vlasov equation with feedback through hitting a boundary," Papers 1808.05311,, revised Aug 2018.
    4. 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.
    5. Alexander Lipton, 2015. "Modern Monetary Circuit Theory, Stability of Interconnected Banking Network, and Balance Sheet Optimization for Individual Banks," Papers 1510.07608,

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