Asymptotic behaviour of randomised fractional volatility models

Understand

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.