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Expensive martingales

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  • Hans Buehler

Abstract

We characterize strictly arbitrage-free markets of European options where only a discrete set of options is traded. We then construct martingales which reprice all given options and which are 'most expensive' among all martingales with this property. We also present algorithms to adjust real-life market data and to construct expensive martingales while taking into account additional 'weak' information: estimated prices of more exotic products such as, for example, forward started options.

Suggested Citation

  • Hans Buehler, 2006. "Expensive martingales," Quantitative Finance, Taylor & Francis Journals, vol. 6(3), pages 207-218.
    • Handle: RePEc:taf:quantf:v:6:y:2006:i:3:p:207-218
    DOI: 10.1080/14697680600668071
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    References listed on IDEAS

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    1. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    2. repec:hum:wpaper:sfb649dp2005-021 is not listed on IDEAS
    3. Härdle, Wolfgang Karl & Hlávka, Zdeněk, 2005. "Dynamics of state price densities," SFB 649 Discussion Papers 2005-021, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    4. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Alexander Cox & Jan Obłój, 2011. "Robust pricing and hedging of double no-touch options," Finance and Stochastics, Springer, vol. 15(3), pages 573-605, September.
    2. Bruno Bouchard & Marcel Nutz, 2013. "Arbitrage and duality in nondominated discrete-time models," Papers 1305.6008, arXiv.org, revised Mar 2015.
    3. Stefan Gerhold & I. Cetin Gulum, 2016. "Consistency of option prices under bid-ask spreads," Papers 1608.05585, arXiv.org, revised Jul 2019.
    4. Papapantoleon Antonis & Yanez Sarmiento Paulo, 2021. "Detection of arbitrage opportunities in multi-asset derivatives markets," Dependence Modeling, De Gruyter, vol. 9(1), pages 439-459, January.
    5. Härdle, Wolfgang & Hlávka, Zdenek, 2009. "Dynamics of state price densities," Journal of Econometrics, Elsevier, vol. 150(1), pages 1-15, May.
    6. Antonis Papapantoleon & Paulo Yanez Sarmiento, 2020. "Detection of arbitrage opportunities in multi-asset derivatives markets," Papers 2002.06227, arXiv.org, revised Nov 2021.
    7. René Carmona & Sergey Nadtochiy, 2009. "Local volatility dynamic models," Finance and Stochastics, Springer, vol. 13(1), pages 1-48, January.
    8. Beatrice Acciaio & Mathias Beiglbock & Friedrich Penkner & Walter Schachermayer, 2013. "A model-free version of the fundamental theorem of asset pricing and the super-replication theorem," Papers 1301.5568, arXiv.org, revised Mar 2013.
    9. Hans Buehler, 2006. "Consistent Variance Curve Models," Finance and Stochastics, Springer, vol. 10(2), pages 178-203, April.
    10. A. Gulisashvili, 2009. "Asymptotic Formulas with Error Estimates for Call Pricing Functions and the Implied Volatility at Extreme Strikes," Papers 0906.0394, arXiv.org.
    11. Henrik Hult & Filip Lindskog & Johan Nykvist, 2013. "A simple time-consistent model for the forward density process," Papers 1301.4869, arXiv.org.
    12. René Carmona & Sergey Nadtochiy, 2012. "Tangent Lévy market models," Finance and Stochastics, Springer, vol. 16(1), pages 63-104, January.

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