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Numerical analysis of an extended structural default model with mutual liabilities and jump risk

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  • Vadim Kaushansky
  • Alexander Lipton
  • Christoph Reisinger

Abstract

We consider a structural default model in an interconnected banking network as in Lipton [International Journal of Theoretical and Applied Finance, 19(6), 2016], with mutual obligations between each pair of banks. We analyse the model numerically for two banks with jumps in their asset value processes. Specifically, we develop a finite difference method for the resulting two-dimensional partial integro-differential equation, and study its stability and consistency. We then compute joint and marginal survival probabilities, as well as prices of credit default swaps (CDS), first-to-default swaps (FTD), credit and debt value adjustments (CVA and DVA). Finally, we calibrate the model to market data and assess the impact of jump risk.

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  • 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.
    • Handle: RePEc:arx:papers:1701.00030
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Karel in 't Hout & Jari Toivanen, 2015. "Application of Operator Splitting Methods in Finance," Papers 1504.01022, arXiv.org.
    4. Leif Andersen & Jesper Andreasen, 2000. "Jump-Diffusion Processes: Volatility Smile Fitting and Numerical Methods for Option Pricing," Review of Derivatives Research, Springer, vol. 4(3), pages 231-262, October.
    5. 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.
    6. Andrey Itkin & Alexander Lipton, 2017. "Structural default model with mutual obligations," Review of Derivatives Research, Springer, vol. 20(1), pages 15-46, April.
    7. 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.
    8. Larry Eisenberg & Thomas H. Noe, 2001. "Systemic Risk in Financial Systems," Management Science, INFORMS, vol. 47(2), pages 236-249, February.
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