It has been recently established that the volatility of financial assets is rough. This means that the behavior of the log-volatility process is similar to that of a fractional Brownian motion with Hurst parameter around 0.1. Motivated by this finding , we wish to define a natural and relevant limit for the fractional Brownian motion when H goes to zero. We show that once properly normalized, the fractional Brownian motion converges to a Gaussian random distribution which is very close to a log-correlated random field.
Rough volatility models are becoming increasingly popular in quantitative finance. In this framework, one considers that the behavior of the log-volatility process of a financial asset is close to that of a fractional Brownian motion with Hurst parameter around 0.1. Motivated by this , we wish to define a natural and relevant limit for the fractional Brownian motion when H goes to zero. We show that once properly normalized, the fractional Brownian motion converges to a Gaussian random distribution which is very close to a log-correlated random field.
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It has been recently established that the volatility of financial assets is rough. This means
Rough volatility models are becoming increasingly popular in quantitative finance. In this framework, one considers
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is similar
of a financial asset is close
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finding