Abstract
Recent evolutions of the business of exotic products has rendered the use of stochastic volatility models necessary. Calibration of single stochastic volatility models has already been discussed in several articles. The purpose of this paper is to build a parameterization of the correlation matrix of a multidimensional model with stochastic volatility, given that:1. The correlation between each asset and its volatility is specified.2. The correlations between different assets are specified.In the following, we propose a parameterization of the set satisfying the two constraints. This parameterization can be used to calibrate the correlations between single underlying models, and provides a range of attainable prices for standard exotic products.
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