# On a Constrained Fractional Stochastic Volatility Model

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.
Keywords :
Document type :
Preprints, Working Papers, ...
Domain :

Cited literature [21 references]

https://hal.archives-ouvertes.fr/hal-01738234
Contributor : Nicolas Marie Connect in order to contact the contributor
Submitted on : Tuesday, March 20, 2018 - 1:03:20 PM
Last modification on : Wednesday, November 3, 2021 - 9:49:01 AM
Long-term archiving on: : Tuesday, September 11, 2018 - 9:24:29 AM

### File

On_a_Constrained_Fractional_St...
Files produced by the author(s)

### Identifiers

• HAL Id : hal-01738234, version 1

### Citation

Nicolas Marie. On a Constrained Fractional Stochastic Volatility Model. 2018. ⟨hal-01738234⟩

Record views