Weak error rates for numerical schemes of non-singular Stochastic Volterra equations with application to stochastic volatility models

Abstract

We study the weak error rate for the Euler-Maruyama scheme for Stochastic Volterra equations (SVE) with application to pricing under stochastic volatility models. SVEs are non-Markovian stochastic differential equations with memory kernel. We assume in particular that the kernel is non-singular and $\mathcal{C}^4$. We show that the weak error rate is of order $O(1/N)$ where $N$ is the number of steps of the Euler-Maruyama scheme, thus giving the same weak error rate as for SDEs. Our proof consists in adapting the classic weak error proof for Markov processes to SVEs; to this end we rely on infinite dimensional functionals and on their derivatives.

Pierre Bras

PhD Student in Applied Mathematics

I am a PhD student under the direction of Gilles Pagès, interested in Machine Learning, Stochastic Optimization and Numerical Probability.