The order barrier for strong approximation of rough volatility models

URL:	https://arxiv.org/abs/1606.03854
Dokumenttyp:	Arbeitspapier
Erscheinungsjahr:	2016
Ort der Veröffentlichung:	Ithaca, NY
Verlag:	Cornell University
Sprache der Veröffentlichung:	Englisch
Einrichtung:	Fakultät für Wirtschaftsinformatik und Wirtschaftsmathematik > Wirtschaftsmathematik II: Stochastische Numerik (Neuenkirch 2013-)
Fachgebiet:	510 Mathematik
Abstract:	We study the strong approximation of a rough volatility model, in which the log-volatility is given by a fractional Ornstein-Uhlenbeck process with Hurst parameter H<1/2. Our methods are based on an equidistant discretization of the volatility process and of the driving Brownian motions, respectively. For the root mean-square error at a single point the optimal rate of convergence that can be achieved by such methods is n−H, where n denotes the number of subintervals of the discretization. This rate is in particular obtained by the Euler method and an Euler-trapezoidal type scheme.