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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. 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.
    3. Constantinos Kardaras, 2012. "Market viability via absence of arbitrage of the first kind," Finance and Stochastics, Springer, vol. 16(4), pages 651-667, October.
    4. 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.
    5. Alexander Cox & David Hobson, 2005. "Local martingales, bubbles and option prices," Finance and Stochastics, Springer, vol. 9(4), pages 477-492, October.
    6. 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.
    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)

    Citations

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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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