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Vulnerable European and American Options in a Market Model with Optional Hazard Process

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  • Libo Li
  • Ruyi Liu
  • Marek Rutkowski

Abstract

We study the upper and lower bounds for prices of European and American style options with the possibility of an external termination, meaning that the contract may be terminated at some random time. Under the assumption that the underlying market model is incomplete and frictionless, we obtain duality results linking the upper price of a vulnerable European option with the price of an American option whose exercise times are constrained to times at which the external termination can happen with a non-zero probability. Similarly, the upper and lower prices for an vulnerable American option are linked to the price of an American option and a game option, respectively. In particular, the minimizer of the game option is only allowed to stop at times which the external termination may occur with a non-zero probability.

Suggested Citation

  • Libo Li & Ruyi Liu & Marek Rutkowski, 2022. "Vulnerable European and American Options in a Market Model with Optional Hazard Process," Papers 2212.12860, arXiv.org.
    • Handle: RePEc:arx:papers:2212.12860
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    References listed on IDEAS

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    1. Kardaras, Constantinos, 2014. "On the characterisation of honest times that avoid all stopping times," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 373-384.
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    4. Miryana Grigorova & Peter Imkeller & Elias Offen & Youssef Ouknine & Marie-Claire Quenez, 2015. "Reflected BSDEs when the obstacle is not right-continuous and optimal stopping," Papers 1504.06094, arXiv.org, revised May 2017.
    5. Roxana Dumitrescu & Marie-Claire Quenez & Agn`es Sulem, 2015. "Game options in an imperfect market with default," Papers 1511.09041, arXiv.org, revised Jul 2017.
    6. Alex Szimayer, 2005. "Valuation of American options in the presence of event risk," Finance and Stochastics, Springer, vol. 9(1), pages 89-107, January.
    7. Libo Li & Ruyi Liu & Marek Rutkowski, 2022. "Well-posedness and penalization schemes for generalized BSDEs and reflected generalized BSDEs," Papers 2212.12854, arXiv.org.
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    9. Choulli, Tahir & Yansori, Sina, 2022. "Explicit description of all deflators for market models under random horizon with applications to NFLVR," Stochastic Processes and their Applications, Elsevier, vol. 151(C), pages 230-264.
    10. Miryana Grigorova & Marie-Claire Quenez & Agnès Sulem, 2020. "European options in a non-linear incomplete market model with default," Post-Print hal-02025833, HAL.
    11. Grigorova, Miryana & Quenez, Marie-Claire & Sulem, Agnès, 2021. "American options in a non-linear incomplete market model with default," Stochastic Processes and their Applications, Elsevier, vol. 142(C), pages 479-512.
    12. Kardaras, Constantinos, 2015. "On the stochastic behaviour of optional processes up to random times," LSE Research Online Documents on Economics 64965, London School of Economics and Political Science, LSE Library.
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    Cited by:

    1. Libo Li & Ruyi Liu & Marek Rutkowski, 2022. "Well-posedness and penalization schemes for generalized BSDEs and reflected generalized BSDEs," Papers 2212.12854, arXiv.org.

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