Cubature Method for Stochastic Volterra Integral Equations

In this paper, we introduce the cubature formulas for Stochastic Volterra Integral Equations. We first derive the stochastic Taylor expansion in this setting and provide its tail estimates. We then introduce the cubature measure for such equations, and construct it explicitly in some special cases, including a long memory stochastic volatility model. Finally, we illustrate its efficiency by presenting several numerical examples.