On moment non-explosions for Wishart-based stochastic volatility models

•Provide parameter conditions ensuring moment non-explosions for equity models.•Apply to the Wishart affine stochastic volatility model.•Apply to the Wishart multidimensional stochastic volatility model.•Show that calibrated parameters are compatible with the constraints.

This paper provides a result on moment non-explosions for a stock following a Wishart multidimensional stochastic volatility dynamics or a Wishart affine stochastic correlation dynamics when the parameter values satisfy certain constraints. By reformulating the stock dynamics in terms of the volatility path along with standard results on matrix Lyapunov and Riccati equations, a non-explosion result of the moment of order greater than one can be obtained. It extends to these frameworks a property well known for the Heston model.