Extending the vast library of univariate models to price multi-asset derivatives is still a challenge in the field of Quantitative Finance. Within the literature on multivariate modelling, a dichotomy may be noticed. On one hand, the focus has been on the construction of models displaying stochastic correlation within the framework of discussion processes (see e.g. Pigorsh and Stelzer (2008), Hubalek and Nicolato (2008) and Zhu (2000)). On the other hand a number of authors have proposed multivariate Levy models, which allow for flexible modelling of returns, but at the expenses of a constant correlation structure (see e.g. Leoni and Schoutens (2007) and Leoni and Schoutens (2007) among others). Tractable multivariate models displaying flexible and stochastic correlation structures combined with jumps is proving to be rather problematic. In particular, the classical technique of introducing stochastic volatility via time-change is quite ineffective when applied to the multivariate setting. In this work we propose a new class of models, which is obtained by conditioning a multivariate Brownian Motion to a so-called matrix subordinator. The obtained model-class encompasses the vast majority of previously proposed models and displays a high degree of flexibility combined with analytical tractability.
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Quantitative Methods in Finance Conference (QMF), 2009