Before revision:  We introduce a novel multi-factor stochastic volatility Heston-based model, which is able to reproduce consistently typical multi-dimensional FX vanilla markets, while retaining the (semi)-analytical tractability typical of affine models and relying on a reasonable number of parameters.
After revision:  We introduce a novel multi-factor Heston-based stochastic volatility model, which is able to reproduce consistently typical multi-dimensional FX vanilla markets, while retaining the (semi)-analytical tractability typical of affine models and relying on a reasonable number of parameters.