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Negative call prices

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  • Johannes Ruf

Abstract

We show that the existence of an equivalent local martingale measure for asset prices does not prevent negative prices for European calls written on positive stock prices. In particular, we illustrate that many standard no-arbitrage arguments implicitly rely on conditions stronger than the No Free Lunch With Vanishing Risk (NFLVR) assumption. The discrepancy between replicating prices and market prices for a contingent claim may be observed in a model satisfying NFLVR since certain trading strategies of buying one portfolio and selling another one are often excluded by standard admissibility constraints. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Johannes Ruf, 2013. "Negative call prices," Annals of Finance, Springer, vol. 9(4), pages 787-794, November.
    • Handle: RePEc:kap:annfin:v:9:y:2013:i:4:p:787-794
    DOI: 10.1007/s10436-012-0221-2
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    References listed on IDEAS

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    1. 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.
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    3. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    4. Alexander Cox & David Hobson, 2005. "Local martingales, bubbles and option prices," Finance and Stochastics, Springer, vol. 9(4), pages 477-492, October.
    5. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    6. 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.
    7. 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.
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    Citations

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    Cited by:

    1. Travis Fisher & Sergio Pulido & Johannes Ruf, 2015. "Financial Models with Defaultable Num\'eraires," Papers 1511.04314, arXiv.org, revised Oct 2017.
    2. Peter Carr & Travis Fisher & Johannes Ruf, 2014. "On the hedging of options on exploding exchange rates," Finance and Stochastics, Springer, vol. 18(1), pages 115-144, January.
    3. Hardy Hulley & Johannes Ruf, 2019. "Weak Tail Conditions for Local Martingales," Published Paper Series 2019-2, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    4. Nikolai Dokuchaev, 2018. "On the implied market price of risk under the stochastic numéraire," Annals of Finance, Springer, vol. 14(2), pages 223-251, May.
    5. Travis Fisher & Sergio Pulido & Johannes Ruf, 2017. "Financial Models with Defaultable Numéraires," Working Papers hal-01240736, HAL.
    6. Laurence Carassus & Emmanuel L'epinette, 2021. "Pricing without no-arbitrage condition in discrete time," Papers 2104.02688, arXiv.org.
    7. Martin HERDEGEN & Martin SCHWEIZER, 2016. "Economically Consistent Valuations and Put-Call Parity," Swiss Finance Institute Research Paper Series 16-02, Swiss Finance Institute.
    8. Martin Herdegen & Martin Schweizer, 2018. "Semi‐efficient valuations and put‐call parity," Mathematical Finance, Wiley Blackwell, vol. 28(4), pages 1061-1106, October.

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    More about this item

    Keywords

    Pricing; Hedging; Arbitrage; Admissibility ; NFLVR; Contingent claim; Strict local martingale; G13;
    All these keywords.

    JEL classification:

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

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