Tous les séminaires
Lundi 23 janvier 2017
Intervenant : Matthieu ROSENBAUM ( Ecole Polytechnique)
« Volatility is rough »
De 15h à 16h15, en salle 08 à l'ENSAE : 3, avenue Pierre Larousse 92240 Malakoff (Tram T3 : « Porte de Vanves » ou Métro 13 : « Porte de Vanves » ou « Malakoff Plateau de Vanves »).
Estimating volatility from recent high frequency data, we revisit the question of the smoothness of the volatility process. Our main result is that log-volatility behaves essentially as a fractional Brownian motion with Hurst exponent H of order 0.1, at any reasonable time scale. This leads us to adopt the fractional stochastic volatility (FSV) model of Comte and Renault. We call our model Rough FSV (RFSV) to underline that, in contrast to FSV, H<1/2. We demonstrate that our RFSV model is remarkably consistent with financial time series data; one application is that it enables us to obtain improved forecasts of realized volatility. Furthermore, we find that although volatility is not long memory in the RFSV model, classical statistical procedures aiming at detecting volatility persistence tend to conclude the presence of long memory in data generated from it. This sheds light on why long memory of volatility has been widely accepted as a stylized fact. Finally, we provide a quantitative market microstructure-based foundation for our findings.
This is joint work with Jim Gatheral and Thibault Jaisson.
Ce séminaire est organisé par :
Alexandre TSYBAKOV (Laboratoire de Statistique-CREST)
Cristina BUTUCEA (Laboratoire de Statistique-CREST)