Parametrization of Correlations in Multi-Stochastic Volatility/Local-Stochastic Volatility Models

When designing multi-asset stochastic volatility (SV) or local-stochastic volatility (LSV) models, one of the main issues involves the construction of the global correlation matrix. Typically correlation matrices for each assets' degrees of freedom are set and the challenge is to build a global correlation matrix which at least recovers these individual correlation matrices, is positive, and is a smooth function of inputs, so that meaningful sensitivities can be calculated.We present a general methodology for constructing such correlation matrices that uses few parameters, is based on correlations of physical observables, applies to both SVs and LSVs, and works regardless of the dimensionality of the single-asset SV/LSV model