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A Framework for Derivative Pricing in the Fractional Black-Scholes Market

  • Ciprian Necula

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

The aim of this paper is to develop a framework for evaluating derivatives if the underlying of the derivative contract is supposed to be driven by a fractional Brownian motion with Hurst parameter greater than 0.5. For this purpose we first prove some results regarding the quasi-conditional expectation, especially the behavior to a Girsanov transform. We obtain the risk-neutral valuation formula and the fundamental evaluation equation in the case of the fractional Black-Scholes market.

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File URL: http://www.dofin.ase.ro/carfib/wpaefr/wpaefr_19.pdf
File Function: First version, 2008
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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 19.

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Date of creation: Oct 2008
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Handle: RePEc:cab:wpaefr:19
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  1. L. C. G. Rogers, 1997. "Arbitrage with Fractional Brownian Motion," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 95-105.
  2. 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 637-54, May-June.
  3. 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.
  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. 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.
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