Solving Black-Schole Equation Using Standard Fractional Brownian Motion

Didier Alain Njamen Njomen and Eric Djeutcha

Journal of Mathematics Research, 2019, vol. 11, issue 2, 142-157

Abstract: In this paper, we emphasize the Black-Scholes equation using standard fractional Brownian motion BHwith the hurst index H ∈ [0,1]. N. Ciprian (Necula, C. (2002)) and Bright and Angela (Bright, O., Angela, I., & Chukwunezu (2014)) get the same formula for the evaluation of a Call and Put of a fractional European with the different approaches. We propose a formula by adapting the non-fractional Black-Scholes model using a λHfactor to evaluate the european option. The price of the option at time t ∈]0,T[ depends on λH(T − t), and the cost of the action St, but not only from t − T as in the classical model. At the end, we propose the formula giving the implied volatility of sensitivities of the option and indicators of the financial market.

Keywords: stock price; black-Scholes model; fractional Brownian motion; options; volatility (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:ibn:jmrjnl:v:11:y:2019:i:2:p:142

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