Multivariate Modelling via Matrix Subordination

TY - CONF

T1 - Multivariate Modelling via Matrix Subordination

AU - Nicolato, Elisa

PY - 2009

Y1 - 2009

N2 - 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 structurescombined 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.

AB - 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 structurescombined 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.

M3 - Paper

T2 - Quantitative Methods in Finance Conference (QMF)

Y2 - 16 December 2009 through 19 December 2009

ER -