The order barrier for strong approximation of rough volatility models

Neuenkirch, Andreas ; Shalaiko, Taras

Document Type: Working paper
Year of publication: 2016
Place of publication: Ithaca, NY
Publishing house: Cornell University
Publication language: English
Institution: School of Business Informatics and Mathematics > Wirtschaftsmathematik II (Neuenkirch 2013-)
Subject: 510 Mathematics
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.

Dieser Eintrag ist Teil der Universitätsbibliographie.

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