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

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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.

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File URL: http://www.dofin.ase.ro/carfib/wpaefr/wpaefr_20.pdf
File Function: First version, 2008
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Bibliographic Info

Paper provided by Bucharest University of Economics, Center for Advanced Research in Finance and Banking - CARFIB in its series Advances in Economic and Financial Research - DOFIN Working Paper Series with number 20.

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Date of creation: Oct 2008
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Handle: RePEc:cab:wpaefr:20

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Related research

Keywords: fractional Brownian motion; fractional Black-Scholes market; the reflection principle for the fractional Brownian motion; mathematical finance; European option; barrier option;

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  1. 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.
  2. 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.
  3. L. C. G. Rogers, 1997. "Arbitrage with Fractional Brownian Motion," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 95-105.
  4. 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.
  5. 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.
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