Applying the IR statistic to estimate the Hurst index of the fractional geometric Brownian motion

Abstract

In 2010 J.M. Bardet and D. Surgailis [1] have introduced the increment ratio (IR) statistic which measures the roughness of random paths. It was shown that this statistic was applicable in the cases of diffusion processes driven by the standard Brownian motion, certain Gaussian processes and the Lévy process. This paper shows that the IR statistic can be applied to estimate the Hurst index H of the fractional geometric Brownian motion.

Keywords

• increment ratio statistic
• fractional geometric Brownian motion
• fractional Black– Scholes model
• Hurst index estimation