A fast algorithm for simulation of rough volatility models. Issue 3 (4th March 2022)

• Record Type: Journal Article
• Authors: Ma, Jingtang; Wu, Haofei
• Is Part Of: Quantitative finance. Volume 22:Issue 3(2022)
• Page Start: 447
• Page End: 462
• Publication Date: 2022-03-04
• Subjects: Rough Heston models -- Fractional Brownian motion -- Fast simulation algorithms -- Monte-Carlo methods -- Regime switching; G13 -- C02; Finance -- Periodicals; Business mathematics -- Periodicals; Finance -- Mathematical models -- Periodicals; Investments -- Mathematics -- Periodicals; Economics -- Periodicals; Finances -- Modèles mathématiques -- Périodiques; 332.015118
• DOI: 10.1080/14697688.2021.1970213
• Languages: English
• ISSNs: 1469-7688

Abstract

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 ) to O ( N log ⁡ N ) or O ( N log 2 ⁡ 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.