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Arbitrage-free pricing of multi-person game claims in discrete time

Author

Listed:
  • Ivan Guo

    (Monash University)

  • Marek Rutkowski

    (University of Sydney
    Warsaw University of Technology)

Abstract

We introduce a class of financial contracts involving several parties by extending the notion of a two-person game option to a contract in which an arbitrary number of parties is involved and each of them is allowed to make a wide array of decisions at any time, not restricted to simply exercising the option. The collection of decisions by all parties then determines the contract’s termination date as well as the terminal payoff for each party. We provide sufficient conditions under which a discrete-time multi-person game option has a unique arbitrage-free price, which is additive with respect to any partition of the contract. Our results are illustrated by the detailed study of a particular multi-person contract with puttable tranches.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:finsto:v:21:y:2017:i:1:d:10.1007_s00780-016-0315-1
    DOI: 10.1007/s00780-016-0315-1
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    References listed on IDEAS

    as
    1. 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.
    2. Andreas Kyprianou, 2004. "Some calculations for Israeli options," Finance and Stochastics, Springer, vol. 8(1), pages 73-86, January.
    3. Jan Kallsen & Christoph Kühn, 2004. "Pricing derivatives of American and game type in incomplete markets," Finance and Stochastics, Springer, vol. 8(2), pages 261-284, May.
    4. Yuri Kifer, 2000. "Game options," Finance and Stochastics, Springer, vol. 4(4), pages 443-463.
    5. Said Hamadène & Mohammed Hassani, 2014. "The multi-player nonzero-sum Dynkin game in discrete time," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 79(2), pages 179-194, April.
    6. Nie, Tianyang & Rutkowski, Marek, 2014. "Multi-player stopping games with redistribution of payoffs and BSDEs with oblique reflection," Stochastic Processes and their Applications, Elsevier, vol. 124(8), pages 2672-2698.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Multi-person games; Arbitrage-free pricing; Optimal equilibrium;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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