Asymptotics for Volatility Derivatives in Multi-Factor Rough Volatility Models

28 Pages Posted: 1 Apr 2019

See all articles by Chloe Lacombe

Chloe Lacombe

Imperial College London

Aitor Muguruza

Imperial College London; Kaiju Capital Management

Henry Stone

Department of Mathematics, Imperial College London

Date Written: March 7, 2019

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.

Keywords: rough volatility,VIX, large deviations, realized variance, small-time asymptotics, Gaussian measure, reproducing kernel Hilbert space

Suggested Citation

Lacombe, Chloe and Muguruza, Aitor and Stone, Henry, Asymptotics for Volatility Derivatives in Multi-Factor Rough Volatility Models (March 7, 2019). Available at SSRN: https://ssrn.com/abstract=3349005 or http://dx.doi.org/10.2139/ssrn.3349005

Chloe Lacombe

Imperial College London ( email )

South Kensington Campus
Imperial College
LONDON, SW7 2AZ
United Kingdom

Aitor Muguruza (Contact Author)

Imperial College London ( email )

South Kensington Campus
Exhibition Road
London, Greater London SW7 2AZ
United Kingdom

Kaiju Capital Management ( email )

Henry Stone

Department of Mathematics, Imperial College London ( email )

South Kensington Campus
Imperial College
LONDON, SW7 2AZ
United Kingdom

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