# Asymptotics for volatility derivatives in multi-factor rough volatility models

## TL;DR

This paper derives small-time implied volatility asymptotics for realized variance and VIX options in multi-factor rough volatility models, providing numerical methods, density approximations, and insights into smile convexity.

## Contribution

It introduces a large deviations framework for rough volatility models, develops efficient numerical recipes, and analyzes how multi-factor constructions influence implied volatility smiles.

## Key findings

- Numerical recipes for rate function computation
- Close-form density approximations for realized variance
- Identification of models producing non-linear smiles around-the-money

## Abstract

We present small-time implied volatility asymptotics for Realised Variance (RV) and VIX options for a number of (rough) stochastic volatility models via large deviations principle. We provide numerical results along with efficient and robust numerical recipes to compute the rate function; the backbone of our theoretical framework. Based on our results, we further develop approximation schemes for the density of RV, which in turn allows to express the volatility swap in close-form. Lastly, we investigate different constructions of multi-factor models and how each of them affects the convexity of the implied volatility smile. Interestingly, we identify the class of models that generate non-linear smiles around-the-money.