Rough Volatility

Specialeforsvar ved Aske Grønborg-Kock

Titel: Rough Volatility

Abstract: In this thesis the properties of a fractional Brownian motion is examined and it is shown that it is natural to model log-volatility by such a process. By a general change of measure the rough Bergomi model is derived and examined throughout this thesis. A hybrid scheme is constructed to increase computational efficiency of simulating the Volterra Process present in the model. Then four different ways to reduce computation time and variance of implied volatility estimators are presented and combined into a single variance minimized estimator. The rough Bergomi model is calibrated to an empirical volatility surface and performance is compared to a similar calibration of the Heston model. Finally both models are calibrated across several dates and compared against each other

Vejleder:  Rolf Poulsen
Censor:    David Sloth Petersen, Danske Bank