Rough Volatility

Specialeforsvar ved Sigurd Emil Rømer

Titel: Rough Volatility

Abstract: In this thesis we investigate volatility on the S&P 500 using high frequency trade data on the SPY. We show that log-volatility is a rough, unifractal process that is approximately Gaussian when aggregated. Based on these findings we propose to model volatility via a fractional Brownian motion with a Hurst exponent H less than 1/2. Under a deterministic change of measure this leads to the rough Bergomi pricing model. For this model we investigate methods for speeding up Monte Carlo estimation and present a fast calibration scheme using various approximations. Calibrating to SPX option prices we find that the model is able to capture the power-law decay of skew observed in practise. We furthermore consider hedging in the model on forward variance curve form and relate the static properties of a power-law decay of skew to the dynamic properties as measured through the skew-stickiness-ratio (SSR). We find that the model with empirically relevant values of H is able to capture the typically observed SSR values of around 1.5. Finally we present some initial thoughts on how one can bet on H in the rough Bergomi model.

Vejleder: Rolf Poulsen
Censor: Thomas Kokholm