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Arbitrage-free pricing of American options in nonlinear markets

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  • Edward Kim
  • Tianyang Nie
  • Marek Rutkowski

Abstract

We re-examine and extend the findings from the recent paper by Dumitrescu, Quenez and Sulem (2018) who studied American and game options in a particular market model using the nonlinear arbitrage-free pricing approach developed in El Karoui and Quenez (1997). In the first part, we provide a detailed study of unilateral valuation problems for the two counterparties in an American-style contract within the framework of a general nonlinear market. We extend results from Bielecki and Rutkowski (2015) and Bielecki, Cialenco and Rutkowski (2018) who examined the case of a European-style contract. In the second part, we present a BSDE approach, which is used to establish more explicit pricing, hedging and exercising results when solutions to reflected BSDEs have additional desirable properties.

Suggested Citation

  • Edward Kim & Tianyang Nie & Marek Rutkowski, 2018. "Arbitrage-free pricing of American options in nonlinear markets," Papers 1804.10753, arXiv.org, revised Jul 2018.
    • Handle: RePEc:arx:papers:1804.10753
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    References listed on IDEAS

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    1. Bayraktar, Erhan & Yao, Song, 2012. "Quadratic reflected BSDEs with unbounded obstacles," Stochastic Processes and their Applications, Elsevier, vol. 122(4), pages 1155-1203.
    2. 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.
    3. Tomasz R. Bielecki & Igor Cialenco & Marek Rutkowski, 2017. "Arbitrage-Free Pricing Of Derivatives In Nonlinear Market Models," Papers 1701.08399, arXiv.org, revised Apr 2018.
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    Cited by:

    1. Junbeom Lee & Chao Zhou, 2021. "Binary funding impacts in derivative valuation," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 242-278, January.

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