Numerical Algorithms For Simulation Of Fractional Volatility Models

A fractional volatility model contains a stochastic Volterra integral with weakly singular kernel.The classical Euler-Maruyama algorithm is not very efficient to simulate this kind of models because it needs to keep records of all the past path-values and thus the computational complexity is too large.This thesis develops a fast two-step iteration algorithm using the approximation of the weakly singular kernel with a sum of exponential functions.Compared to Euler-Maruyama algorithm,the complexity of the fast algorithm is reduced from O(N2)to O(N log N)or O(N log2 N)for simulating one path,where N is the number of time steps.Meanwhile,the fast algorithm is developed to simulate the rough Heston models with(without)regime switching,and the multi-factor approximation algorithms are also studied and compared.A number of numerical examples are carried out to confirm the high efficiency of the proposed algorithm.