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Pricing European and Barrier Options in the Fractional Black-Scholes Market

Author

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  • Ciprian Necula

    (Faculty of Finance and Banking, Bucharest University of Economics)

Abstract

The aim of this paper is to obtain the valuation formulas for European and barrier options if the underlying of the option contract is supposed to be driven by a fractional Brownian motion with Hurst parameter greater than 0.5. The paper is build upon the framework developed in Necula (2007) for the valuation of derivative products in the fractional Black-Scholes market. We also obtain a reflection principle for the fractional Brownian motion.

Suggested Citation

  • Ciprian Necula, 2008. "Pricing European and Barrier Options in the Fractional Black-Scholes Market," Advances in Economic and Financial Research - DOFIN Working Paper Series 20, Bucharest University of Economics, Center for Advanced Research in Finance and Banking - CARFIB.
    • Handle: RePEc:cab:wpaefr:20
    as

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    File URL: http://www.dofin.ase.ro/carfib/wpaefr/wpaefr_20.pdf
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    References listed on IDEAS

    as
    1. Cipian Necula, 2008. "Barrier Options and a Reflection Principle of the Fractional Brownian Motion," Advances in Economic and Financial Research - DOFIN Working Paper Series 6, Bucharest University of Economics, Center for Advanced Research in Finance and Banking - CARFIB.
    2. Ciprian Necula, 2008. "A Framework for Derivative Pricing in the Fractional Black-Scholes Market," Advances in Economic and Financial Research - DOFIN Working Paper Series 19, Bucharest University of Economics, Center for Advanced Research in Finance and Banking - CARFIB.
    3. Alòs, Elisa & Mazet, Olivier & Nualart, David, 2000. "Stochastic calculus with respect to fractional Brownian motion with Hurst parameter lesser than," Stochastic Processes and their Applications, Elsevier, vol. 86(1), pages 121-139, March.
    4. L. C. G. Rogers, 1997. "Arbitrage with Fractional Brownian Motion," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 95-105, January.
    5. Cipian Necula, 2008. "Option Pricing in a Fractional Brownian Motion Environment," Advances in Economic and Financial Research - DOFIN Working Paper Series 2, Bucharest University of Economics, Center for Advanced Research in Finance and Banking - CARFIB.
    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.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    fractional Brownian motion; fractional Black-Scholes market; the reflection principle for the fractional Brownian motion; mathematical finance; European option; barrier option;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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