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Arbitrage pricing of defaultable game options with applications to convertible bonds

Author

Listed:
  • Tomasz Bielecki
  • Stephane Crepey
  • Monique Jeanblanc
  • Marek Rutkowski

Abstract

This paper is the first in a series that we devote to studying the problems of valuation and hedging of defaultable game options in general, and convertible corporate bonds in particular. Here, we present mathematical foundations for our overall study. Specifically, we provide several results characterizing the arbitrage price of a defaultable game option in terms of relevant Dynkin games. In addition, we provide important results regarding price decomposition of defaultable options. These general results are then specified to the case of convertible bonds, yielding in particular a decomposition of convertible bonds in an optional and a bond component.

Suggested Citation

  • 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.
  • Handle: RePEc:taf:quantf:v:8:y:2008:i:8:p:795-810
    DOI: 10.1080/14697680701401083
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    Citations

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    Cited by:

    1. Christopher Beveridge & Mark Joshi, 2011. "Monte Carlo Bounds for Game Options Including Convertible Bonds," Management Science, INFORMS, vol. 57(5), pages 960-974, May.
    2. Alet Roux, 2015. "Pricing and hedging game options in currency models with proportional transaction costs," Papers 1504.07920, arXiv.org, revised Aug 2015.
    3. Ivan Guo & Marek Rutkowski, 2017. "Arbitrage-free pricing of multi-person game claims in discrete time," Finance and Stochastics, Springer, vol. 21(1), pages 111-155, January.
    4. Alet Roux, 2016. "Pricing And Hedging Game Options In Currency Models With Proportional Transaction Costs," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(07), pages 1-25, November.
    5. Yuri Kifer, 2012. "Dynkin Games and Israeli Options," Papers 1209.1791, arXiv.org.
    6. Yagi, Kyoko & Sawaki, Katsushige, 2010. "The pricing and optimal strategies of callable warrants," European Journal of Operational Research, Elsevier, vol. 206(1), pages 123-130, October.
    7. Egami, Masahiko & Leung, Tim & Yamazaki, Kazutoshi, 2013. "Default swap games driven by spectrally negative Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 123(2), pages 347-384.
    8. Huiwen Yan & Zhou Yang & Fahuai Yi & Gechun Liang, 2015. "Dynkin Game of Convertible Bonds and Their Optimal Strategy," Papers 1503.08961, arXiv.org.
    9. Weijie Pang & Stephan Sturm, 2020. "XVA Valuation under Market Illiquidity," Papers 2011.03543, arXiv.org.
    10. Alet Roux & Tomasz Zastawniak, 2016. "Game options with gradual exercise and cancellation under proportional transaction costs," Papers 1612.02312, arXiv.org.
    11. Gechun Liang & Haodong Sun, 2018. "Dynkin games with Poisson random intervention times," Papers 1803.00329, arXiv.org, revised Jul 2019.
    12. Tianyang Nie & Edward Kim & Marek Rutkowski, 2018. "Arbitrage-Free Pricing of Game Options in Nonlinear Markets," Papers 1807.05448, arXiv.org.
    13. Agostino Capponi & Jose Figueroa-Lopez & Jeffrey Nisen, 2011. "Pricing and Semimartingale Representations of Vulnerable Contingent Claims in Regime-Switching Markets," Papers 1110.0403, arXiv.org, revised Feb 2012.
    14. Rida Laraki & Eilon Solan, 2012. "Equilibrium in Two-Player Nonzero-Sum Dynkin Games in Continuous Time," Working Papers hal-00753508, HAL.
    15. Ivan Guo & Marek Rutkowski, 2014. "Arbitrage Pricing of Multi-person Game Contingent Claims," Papers 1405.2718, arXiv.org.
    16. David Hobson & Gechun Liang & Haodong Sun, 2021. "Callable convertible bonds under liquidity constraints," Papers 2111.02554, arXiv.org.

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