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Default Swap Games Driven by Spectrally Negative Levy Processes

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  • Masahiko Egami
  • Tim S. T. Leung
  • Kazutoshi Yamazaki

Abstract

This paper studies game-type credit default swaps that allow the protection buyer and seller to raise or reduce their respective positions once prior to default. This leads to the study of an optimal stopping game subject to early default termination. Under a structural credit risk model based on spectrally negative Levy processes, we apply the principles of smooth and continuous fit to identify the equilibrium exercise strategies for the buyer and the seller. We then rigorously prove the existence of the Nash equilibrium and compute the contract value at equilibrium. Numerical examples are provided to illustrate the impacts of default risk and other contractual features on the players' exercise timing at equilibrium.

Suggested Citation

  • Masahiko Egami & Tim S. T. Leung & Kazutoshi Yamazaki, 2011. "Default Swap Games Driven by Spectrally Negative Levy Processes," Papers 1105.0238, arXiv.org, revised Sep 2012.
    • Handle: RePEc:arx:papers:1105.0238
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    1. Dilip B. Madan & Peter P. Carr & Eric C. Chang, 1998. "The Variance Gamma Process and Option Pricing," Review of Finance, European Finance Association, vol. 2(1), pages 79-105.
    2. A. Kyprianou & B. Surya, 2007. "Principles of smooth and continuous fit in the determination of endogenous bankruptcy levels," Finance and Stochastics, Springer, vol. 11(1), pages 131-152, January.
    3. 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.
    4. Dilip B. Madan & Frank Milne, 1991. "Option Pricing With V. G. Martingale Components1," Mathematical Finance, Wiley Blackwell, vol. 1(4), pages 39-55, October.
    5. Tim Siu-Tang Leung & Kazutoshi Yamazaki, 2010. "American Step-Up and Step-Down Default Swaps under Levy Models," Papers 1012.3234, arXiv.org, revised Sep 2012.
    6. Bianca Hilberink & L.C.G. Rogers, 2002. "Optimal capital structure and endogenous default," Finance and Stochastics, Springer, vol. 6(2), pages 237-263.
    7. Tomasz Bielecki & Stephane Crepey & Monique Jeanblanc & Marek Rutkowski, 2008. "Arbitrage pricing of defaultable game options with applications to convertible bonds," Quantitative Finance, Taylor & Francis Journals, vol. 8(8), pages 795-810.
    8. Andreas Kyprianou, 2004. "Some calculations for Israeli options," Finance and Stochastics, Springer, vol. 8(1), pages 73-86, January.
    9. Masahiko Egami & Kazutoshi Yamazaki, 2010. "Precautionary Measures for Credit Risk Management in Jump Models," Discussion papers e-10-001, Graduate School of Economics Project Center, Kyoto University.
    10. Eberlein, Ernst & Keller, Ulrich & Prause, Karsten, 1998. "New Insights into Smile, Mispricing, and Value at Risk: The Hyperbolic Model," The Journal of Business, University of Chicago Press, vol. 71(3), pages 371-405, July.
    11. Baurdoux, E.J. & Kyprianou, A.E. & Pardo, J.C., 2011. "The Gapeev-Kühn stochastic game driven by a spectrally positive Lévy process," Stochastic Processes and their Applications, Elsevier, vol. 121(6), pages 1266-1289, June.
    12. Carr, Peter, 1998. "Randomization and the American Put," The Review of Financial Studies, Society for Financial Studies, vol. 11(3), pages 597-626.
    13. Biffis, Enrico & Kyprianou, Andreas E., 2010. "A note on scale functions and the time value of ruin for Lévy insurance risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 46(1), pages 85-91, February.
    14. Soeren Asmussen & Dilip Madan & Martijn Pistorius, 2007. "Pricing Equity Default Swaps under an approximation to the CGMY L\'{e}% vy Model," Papers 0711.2807, arXiv.org.
    15. L. Alili & A. E. Kyprianou, 2005. "Some remarks on first passage of Levy processes, the American put and pasting principles," Papers math/0508487, arXiv.org.
    16. Dickson,David C. M., 2010. "Insurance Risk and Ruin," Cambridge Books, Cambridge University Press, number 9780521176750.
    17. Yuri Kifer, 2000. "Game options," Finance and Stochastics, Springer, vol. 4(4), pages 443-463.
    18. Loeffen, R.L., 2009. "An optimal dividends problem with transaction costs for spectrally negative Lévy processes," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 41-48, August.
    19. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
    20. Zhou, Chunsheng, 2001. "The term structure of credit spreads with jump risk," Journal of Banking & Finance, Elsevier, vol. 25(11), pages 2015-2040, November.
    21. Florin Avram & Zbigniew Palmowski & Martijn R. Pistorius, 2007. "On the optimal dividend problem for a spectrally negative L\'{e}vy process," Papers math/0702893, arXiv.org.
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    Cited by:

    1. Mingsi Long & Hongzhong Zhang, 2017. "On the optimality of threshold type strategies in single and recursive optimal stopping under L\'evy models," Papers 1707.07797, arXiv.org, revised Aug 2018.
    2. Tim Leung & Kazutoshi Yamazaki & Hongzhong Zhang, 2015. "An Analytic Recursive Method For Optimal Multiple Stopping: Canadization And Phase-Type Fitting," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(05), pages 1-31.
    3. Baurdoux, Erik J. & Yamazaki, Kazutoshi, 2015. "Optimality of doubly reflected Lévy processes in singular control," Stochastic Processes and their Applications, Elsevier, vol. 125(7), pages 2727-2751.
    4. Hongzhong Zhang, 2018. "Stochastic Drawdowns," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 10078, December.
    5. Baurdoux, Erik J. & Yamazaki, Kazutoshi, 2015. "Optimality of doubly reflected Lévy processes in singular control," LSE Research Online Documents on Economics 61617, London School of Economics and Political Science, LSE Library.
    6. Long, Mingsi & Zhang, Hongzhong, 2019. "On the optimality of threshold type strategies in single and recursive optimal stopping under Lévy models," Stochastic Processes and their Applications, Elsevier, vol. 129(8), pages 2821-2849.
    7. Neofytos Rodosthenous & Hongzhong Zhang, 2017. "Beating the Omega Clock: An Optimal Stopping Problem with Random Time-horizon under Spectrally Negative L\'evy Models," Papers 1706.03724, arXiv.org.
    8. Kazutoshi Yamazaki, 2017. "Inventory Control for Spectrally Positive Lévy Demand Processes," Mathematics of Operations Research, INFORMS, vol. 42(1), pages 212-237, January.
    9. Kazutoshi Yamazaki, 2016. "Optimality of two-parameter strategies in stochastic control," Papers 1605.04995, arXiv.org.
    10. Hernández-Hernández, Daniel & Yamazaki, Kazutoshi, 2015. "Games of singular control and stopping driven by spectrally one-sided Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 125(1), pages 1-38.

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