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Expensive martingales

Author

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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

    as
    1. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    2. Härdle, Wolfgang & Hlávka, Zdenek, 2009. "Dynamics of state price densities," Journal of Econometrics, Elsevier, vol. 150(1), pages 1-15, May.
    3. 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.
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    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.
    4. Härdle, Wolfgang & Hlávka, Zdenek, 2009. "Dynamics of state price densities," Journal of Econometrics, Elsevier, vol. 150(1), pages 1-15, May.
    5. René Carmona & Sergey Nadtochiy, 2009. "Local volatility dynamic models," Finance and Stochastics, Springer, vol. 13(1), pages 1-48, January.
    6. 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.
    7. A. Gulisashvili, 2009. "Asymptotic Formulas with Error Estimates for Call Pricing Functions and the Implied Volatility at Extreme Strikes," Papers 0906.0394, arXiv.org.
    8. Henrik Hult & Filip Lindskog & Johan Nykvist, 2013. "A simple time-consistent model for the forward density process," Papers 1301.4869, arXiv.org.
    9. René Carmona & Sergey Nadtochiy, 2012. "Tangent Lévy market models," Finance and Stochastics, Springer, vol. 16(1), pages 63-104, January.
    10. Hans Buehler, 2006. "Consistent Variance Curve Models," Finance and Stochastics, Springer, vol. 10(2), pages 178-203, April.

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