A fast algorithm for simulation of rough volatility models

Jingtang Ma and Haofei Wu

Quantitative Finance, 2022, vol. 22, issue 3, 447-462

Abstract: A rough volatility model contains a stochastic Volterra integral with a weakly singular kernel. The classical Euler-Maruyama algorithm is not very efficient for simulating this kind of model because one needs to keep records of all the past path-values and thus the computational complexity is too large. This paper develops a fast two-step iteration algorithm using an approximation of the weakly singular kernel with a sum of exponential functions. Compared to the Euler-Maruyama algorithm, the complexity of the fast algorithm is reduced from $ O(N^{2}) $ O(N2) to $ O(N\log N) $ O(Nlog⁡N) or $ O(N\log ^{2} N) $ O(Nlog2⁡N) for simulating one path, where N is the number of time steps. Further, the fast algorithm is developed to simulate rough Heston models with (or without) regime switching, and multi-factor approximation algorithms are also studied and compared. The convergence rates of the Euler-Maruyama algorithm and the fast algorithm are proved. A number of numerical examples are carried out to confirm the high efficiency of the proposed algorithm.

Date: 2022
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DOI: 10.1080/14697688.2021.1970213

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