Asymptotic Behaviour of Randomised Fractional Volatility Models
23 Pages Posted: 7 Aug 2017 Last revised: 15 Jun 2018
Date Written: August 3, 2017
We study the asymptotic behaviour of a class of small-noise diffusions driven by fractional Brownian motion, with random starting points. Different scalings allow for different asymptotic properties of the process (small-time and tail behaviours in particular). In order to do so, we extend some results on sample path large deviations for such diffusions. As an application, we show how these results characterise the small-time and tail estimates of the implied volatility for rough volatility models, recently proposed in mathematical finance.
Keywords: Rough volatility, large deviations, implied volatility asymptotics
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