Efficient simulation of a new class of Volterra-type SDEs

Abstract

We propose a new theoretical framework that exploits convolution kernels to transform a Volterra-type path-dependent (non-Markovian) stochastic process into a standard (Markovian) diffusion process. The transformation is reversible. We discuss existence and path-wise regularity of solutions for our class of stochastic differential equations. In the fractional-kernel case, when $H\in (0,\frac{1}{2})$, where $H$ is the Hurst coefficient, we propose a numerical simulation scheme which exhibits a strong convergence rate of order $1/2$, improving upon the rate typically obtained by Euler schemes for stochastic Volterra equations with comparably rough trajectories. This improvement is made possible by the distinctive structure of the proposed class, characterized by a non-Markovian process whose coefficients are driven by an associated Markovian one.

Previously appearing as "From elephant to goldfish (and back): memory in stochastic Volterra processes"