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2008•RePEc: Research Papers in EconomicsRequires access

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

Ciprian Necula

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Abstract

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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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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Available abstract

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.

Key concepts: Fractional Brownian motion, Reflection principle (Wiener process), Valuation (finance), Hurst exponent, Black–Scholes model, Valuation of options, Geometric Brownian motion, Barrier option

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