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Strict Local Martingale Deflators and Pricing American Call-Type Options

Author

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  • Erhan Bayraktar
  • Constantinos Kardaras
  • Hao Xing

Abstract

We solve the problem of pricing and optimal exercise of American call-type options in markets which do not necessarily admit an equivalent local martingale measure. This resolves an open question proposed by Fernholz and Karatzas [Stochastic Portfolio Theory: A Survey, Handbook of Numerical Analysis, 15:89-168, 2009].

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  • Erhan Bayraktar & Constantinos Kardaras & Hao Xing, 2009. "Strict Local Martingale Deflators and Pricing American Call-Type Options," Papers 0908.1082, arXiv.org, revised Dec 2009.
    • Handle: RePEc:arx:papers:0908.1082
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    File URL: http://arxiv.org/pdf/0908.1082
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    References listed on IDEAS

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    1. Steven L. Heston & Mark Loewenstein & Gregory A. Willard, 2007. "Options and Bubbles," The Review of Financial Studies, Society for Financial Studies, vol. 20(2), pages 359-390.
    2. Alexander Cox & David Hobson, 2005. "Local martingales, bubbles and option prices," Finance and Stochastics, Springer, vol. 9(4), pages 477-492, October.
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    Cited by:

    1. Erhan Bayraktar & Constantinos Kardaras & Hao Xing, 2010. "Valuation equations for stochastic volatility models," Papers 1004.3299, arXiv.org, revised Dec 2011.
    2. Alexander Vervuurt, 2015. "Topics in Stochastic Portfolio Theory," Papers 1504.02988, arXiv.org.
    3. Johannes Ruf, 2013. "Negative call prices," Annals of Finance, Springer, vol. 9(4), pages 787-794, November.
    4. Johannes Ruf, 2012. "Negative Call Prices," Papers 1204.1903, arXiv.org, revised Jan 2013.
    5. Johannes Ruf, 2010. "Hedging under arbitrage," Papers 1003.4797, arXiv.org, revised May 2011.

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