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Arbitrage pricing of defaultable game options with applications to convertible bonds


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


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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    References listed on IDEAS

    1. Acharya, Viral V. & John, Kose & Sundaram, Rangarajan K., 2000. "On the optimality of resetting executive stock options," Journal of Financial Economics, Elsevier, vol. 57(1), pages 65-101, July.
    2. Corrado, Charles J. & Jordan, Bradford D. & Miller, Thomas Jr. & Stansfield, John J., 2001. "Repricing and employee stock option valuation," Journal of Banking & Finance, Elsevier, vol. 25(6), pages 1059-1082, June.
    3. Carter, Mary Ellen & Lynch, Luann J., 2004. "The effect of stock option repricing on employee turnover," Journal of Accounting and Economics, Elsevier, vol. 37(1), pages 91-112, February.
    4. Brenner, Menachem & Sundaram, Rangarajan K. & Yermack, David, 2000. "Altering the terms of executive stock options," Journal of Financial Economics, Elsevier, vol. 57(1), pages 103-128, July.
    5. Johnson, Shane A. & Tian, Yisong S., 2000. "The value and incentive effects of nontraditional executive stock option plans," Journal of Financial Economics, Elsevier, vol. 57(1), pages 3-34, July.
    6. Mark A. Chen, 2004. "Executive Option Repricing, Incentives, and Retention," Journal of Finance, American Finance Association, vol. 59(3), pages 1167-1200, June.
    7. Mark Craddock & David Heath & Eckhard Platen, 1999. "Numerical Inversion of Laplace Transforms: A Survey of Techniques with Applications to Derivative Pricing," Research Paper Series 27, Quantitative Finance Research Centre, University of Technology, Sydney.
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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,, revised Aug 2015.
    3. Alet Roux & Tomasz Zastawniak, 2016. "Game options with gradual exercise and cancellation under proportional transaction costs," Papers 1612.02312,
    4. 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.
    5. 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.
    6. Yuri Kifer, 2012. "Dynkin Games and Israeli Options," Papers 1209.1791,
    7. Agostino Capponi & Jose Figueroa-Lopez & Jeffrey Nisen, 2011. "Pricing and Semimartingale Representations of Vulnerable Contingent Claims in Regime-Switching Markets," Papers 1110.0403,, revised Feb 2012.
    8. Rida Laraki & Eilon Solan, 2012. "Equilibrium in Two-Player Nonzero-Sum Dynkin Games in Continuous Time," Working Papers hal-00753508, HAL.
    9. Ivan Guo & Marek Rutkowski, 2014. "Arbitrage Pricing of Multi-person Game Contingent Claims," Papers 1405.2718,
    10. 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.
    11. 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.
    12. Huiwen Yan & Zhou Yang & Fahuai Yi & Gechun Liang, 2015. "Dynkin Game of Convertible Bonds and Their Optimal Strategy," Papers 1503.08961,


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