The Order Barrier for Strong Approximation of Rough Volatility Models

2016/06/13 by Andreas Neuenkirch, Neuenkirch, Andreas, Taras Shalaiko +1
Economics, Econometrics and Finance · #Complex Systems and Time Series Analysis #FOS: Mathematics #Financial Risk and Volatility Modeling #Numerical Analysis (math.NA) #Probability (math.PR) #Stochastic processes and financial applications

paper · doi:10.48550/arxiv.1606.03854

openalex publication_date 2016/06/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Fractional Brownian Motions, Fractional Noises and Applications

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