On a Constrained Fractional Stochastic Volatility Model

Nicolas Marie

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arXiv · 1608.03421

On a Constrained Fractional Stochastic Volatility Model

Nicolas Marie

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Abstract

This paper deals with an extension of the so-called Black-Scholes model in which the volatility is modeled by a linear combination of the components of the solution of a differential equation driven by a fractional Brownian motion of Hurst parameter greater than $1/4$. In order to ensure the positiveness of the volatility, the coefficients of that equation satisfy a viability condition. The absence of arbitrages, the completeness of the market and a pricing formula are established.

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Nicolas Marie. 2016-08-11. On a Constrained Fractional Stochastic Volatility Model. https://arxiv.org/abs/1608.03421

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