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Valuation and parities for exchange options

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  • Kardaras, Constantinos

Abstract

Valuation and parities for both European-style and American-style exchange options are presented in a general financial model allowing for jumps, the possibility of default, and “bubbles” in asset prices. The formulas are given via expectations of auxiliary probabilities using the change-of-numéraire technique. Extensive discussion is provided regarding the way that folklore results such as Merton's no-early-exercise theorem and traditional parities have to be altered in this more versatile framework.

Suggested Citation

  • Kardaras, Constantinos, 2015. "Valuation and parities for exchange options," LSE Research Online Documents on Economics 65535, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:65535
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    File URL: http://eprints.lse.ac.uk/65535/
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    References listed on IDEAS

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    1. Mark Loewenstein & Gregory A. Willard, 2000. "Local martingales, arbitrage, and viability," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 16(1), pages 135-161.
    2. Erhan Bayraktar & Constantinos Kardaras & Hao Xing, 2012. "Strict local martingale deflators and valuing American call-type options," Finance and Stochastics, Springer, vol. 16(2), pages 275-291, April.
    3. Hardy Hulley, 2010. "The Economic Plausibility of Strict Local Martingales in Financial Modelling," Research Paper Series 279, Quantitative Finance Research Centre, University of Technology, Sydney.
    4. Alexander Cox & David Hobson, 2005. "Local martingales, bubbles and option prices," Finance and Stochastics, Springer, vol. 9(4), pages 477-492, October.
    5. Julien Hugonnier & Dmitry Kramkov & Walter Schachermayer, 2005. "On Utility‐Based Pricing Of Contingent Claims In Incomplete Markets," Mathematical Finance, Wiley Blackwell, vol. 15(2), pages 203-212, April.
    6. Constantinos Kardaras, 2012. "Market viability via absence of arbitrage of the first kind," Finance and Stochastics, Springer, vol. 16(4), pages 651-667, October.
    7. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    8. Margrabe, William, 1978. "The Value of an Option to Exchange One Asset for Another," Journal of Finance, American Finance Association, vol. 33(1), pages 177-186, March.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Travis Fisher & Sergio Pulido & Johannes Ruf, 2019. "Financial Models with Defaultable Numéraires," Post-Print hal-01240736, HAL.
    2. Fisher, Travis & Pulido, Sergio & Ruf, Johannes, 2019. "Financial models with defaultable numéraires," LSE Research Online Documents on Economics 84973, London School of Economics and Political Science, LSE Library.
    3. Travis Fisher & Sergio Pulido & Johannes Ruf, 2015. "Financial Models with Defaultable Num\'eraires," Papers 1511.04314, arXiv.org, revised Oct 2017.
    4. Travis Fisher & Sergio Pulido & Johannes Ruf, 2017. "Financial Models with Defaultable Numéraires," Working Papers hal-01240736, HAL.
    5. Martin HERDEGEN & Martin SCHWEIZER, 2016. "Economically Consistent Valuations and Put-Call Parity," Swiss Finance Institute Research Paper Series 16-02, Swiss Finance Institute.
    6. Martin Herdegen & Martin Schweizer, 2018. "Semi‐efficient valuations and put‐call parity," Mathematical Finance, Wiley Blackwell, vol. 28(4), pages 1061-1106, October.
    7. Travis Fisher & Sergio Pulido & Johannes Ruf, 2019. "Financial models with defaultable numéraires," Mathematical Finance, Wiley Blackwell, vol. 29(1), pages 117-136, January.

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    More about this item

    Keywords

    exchange options; parities; change of numeraire;
    All these keywords.

    JEL classification:

    • F3 - International Economics - - International Finance
    • G3 - Financial Economics - - Corporate Finance and Governance

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