A CLT for Solutions to SVIEs and Their Non-Markovianity

Abstract

In this work, we prove a central limit theorem for the finite-dimensional distributions of solutions to stochastic Volterra integral equations, where we focus on coefficients satisfying linear growth and Hölder conditions. As we consider the (potentially singular) Riemann-Liouville kernel, the Hurst Parameter H>0 plays an essential role in choosing the appropriate normalizing sequence for the CLT. Provided that the density of the solution is sufficiently smooth, we can, moreover, prove the non-Markovianity of the process, which is of importance for applications in mathematical finance as it significantly complicates pricing and hedging of financial derivatives. Joint work with Stefan Gerhold.