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2021•arXiv (Cornell University)Open access

European option pricing under generalized fractional Brownian motion.

Axel A. Araneda

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Abstract

The Generalized fractional Brownian motion (gfBm) is a stochastic process that acts as a generalization for both fractional, sub-fractional, and standard Brownian motion. Here we study its application into the option pricing problem by means of the valuation of a European Call option. By the derivation of the generalized fractional Ito's lemma and the related Fokker-Planck equation, a closed-form pricing formula for both Black-Scholes and CEV models driven by gfBm is obtained.

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The Generalized fractional Brownian motion (gfBm) is a stochastic process that acts as a generalization for both fractional, sub-fractional, and standard Brownian motion. Here we study its application into the option pricing problem by means of the valuation of a European Call option. By the derivation of the generalized fractional Ito's lemma and the related Fokker-Planck equation, a closed-form pricing formula for both Black-Scholes and CEV models driven by gfBm is obtained.

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Available abstract

The Generalized fractional Brownian motion (gfBm) is a stochastic process that acts as a generalization for both fractional, sub-fractional, and standard Brownian motion. Here we study its application into the option pricing problem by means of the valuation of a European Call option. By the derivation of the generalized fractional Ito's lemma and the related Fokker-Planck equation, a closed-form pricing formula for both Black-Scholes and CEV models driven by gfBm is obtained.

Key concepts: Fractional Brownian motion, Generalization, Lemma (botany), Valuation of options, Mathematics, Valuation (finance), Brownian motion, Geometric Brownian motion

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