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Risk preference based option pricing in a fractional Brownian market

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  • Rostek, Stefan
  • Schöbel, Rainer

Abstract

We focus on a preference based approach when pricing options in a market driven by fractional Brownian motion. Within this framework we derive formulae for fractional European options using the traditional idea of conditional expectation. The obtained formulae - as well as further results - accord with classical Brownian theory and con?rm economic intuition towards fractional Brownian motion. Furthermore the in?uence of the Hurst parameter H on the price of a European option will be analyzed.

Suggested Citation

  • Rostek, Stefan & Schöbel, Rainer, 2006. "Risk preference based option pricing in a fractional Brownian market," Tübinger Diskussionsbeiträge 299, University of Tübingen, School of Business and Economics.
    • Handle: RePEc:zbw:tuedps:299
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    Cited by:

    1. Hager, Svenja & Schöbel, Rainer, 2006. "Deriving the dependence structure of portfolio credit derivatives using evolutionary algorithms," Tübinger Diskussionsbeiträge 300, University of Tübingen, School of Business and Economics.
    2. Zaby, Alexandra K., 2009. "The propensity to patent in oligopolistic markets," Tübinger Diskussionsbeiträge 323, University of Tübingen, School of Business and Economics.
    3. Yalcin, Erdal, 2007. "The proximity-concentration trade-off in a dynamic framework," Tübinger Diskussionsbeiträge 312, University of Tübingen, School of Business and Economics.
    4. Felbermayr, Gabriel J. & Toubal, Farid, 2010. "Cultural proximity and trade," European Economic Review, Elsevier, vol. 54(2), pages 279-293, February.
    5. Heger, Diana & Zaby, Alexandra K., 2009. "The propensity to patent with vertically differentiated products: An empirical investigation," Tübinger Diskussionsbeiträge 325, University of Tübingen, School of Business and Economics.
    6. Schüle, Tobias, 2006. "Creditor coordination with social learning and endogenous timing of credit decisions," Tübinger Diskussionsbeiträge 307, University of Tübingen, School of Business and Economics.
    7. Frontczak, Robert & Schöbel, Rainer, 2008. "Pricing American options with Mellin transforms," Tübinger Diskussionsbeiträge 319, University of Tübingen, School of Business and Economics.
    8. Dymke, Björn M. & Walter, Andreas, 2006. "Insider trading in Germany: Do corporate insiders exploit inside information?," Tübinger Diskussionsbeiträge 309, University of Tübingen, School of Business and Economics.
    9. Stoyan V. Stoyanov & Yong Shin Kim & Svetlozar T. Rachev & Frank J. Fabozzi, 2017. "Option pricing for Informed Traders," Papers 1711.09445, arXiv.org.
    10. Brandes, Julia & Schüle, Tobias, 2007. "IMF's assistance: Devil's kiss or guardian angel?," Tübinger Diskussionsbeiträge 310, University of Tübingen, School of Business and Economics.
    11. Heger, Diana & Zaby, Alexandra K., 2009. "The propensity to patent with horizontally differentiated products: An empirical investigation," Tübinger Diskussionsbeiträge 324, University of Tübingen, School of Business and Economics.
    12. Li, Meiyu & Gençay, Ramazan & Xue, Yi, 2016. "Is it Brownian or fractional Brownian motion?," Economics Letters, Elsevier, vol. 145(C), pages 52-55.
    13. Frontczak, Robert, 2009. "Valuing options in Heston's stochastic volatility model: Another analytical approach," Tübinger Diskussionsbeiträge 326, University of Tübingen, School of Business and Economics.
    14. Frontczak, Robert & Schöbel, Rainer, 2009. "On modified Mellin transforms, Gauss-Laguerre quadrature, and the valuation of American call options," Tübinger Diskussionsbeiträge 320, University of Tübingen, School of Business and Economics.
    15. Maier, Ramona & Merz, Michael, 2008. "Credibility theory and filter theory in discrete and continuous time," Tübinger Diskussionsbeiträge 318, University of Tübingen, School of Business and Economics.

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    Keywords

    Fractional Brownian motion; Conditional expectation; Risk preference based option pricing; Fractional option pricing; Fractional Greeks;
    All these keywords.

    JEL classification:

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

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