Hybrid multifactor scheme for stochastic Volterra equations

We present the hybrid-exponential scheme for simulating stochastic Volterra equations. The scheme is based on an exact approximation of the kernel function near the origin and an approximation by a sum of exponentials across the rest of the domain. The first part is similar to the hybrid scheme introduced in and is needed to capture any singular behavior of the kernel. The second part follows the ideas of where rough volatility models are under consideration and results in a number of stochastic factors to be simulated, one for each exponential term, and all with linear complexity in time. Since the efficiency of our scheme relies heavily on ensuring a low number of factors, we include also a review of various methods for finding the exponential terms. We here discover the method of and show that many fewer terms are needed for the rough fractional kernel than previously established in. Lastly, we provide a proof of convergence and also numerically demonstrate the efficiency of the scheme by example on the rough Bergomi model from.