A Multivariate Lévy Process Model with Linear Correlation

In this paper, we develop a multivariate risk-neutral Lévy process model and discuss its applicabilityin the context of the volatility smile of multiple assets. Our formulation is based upona linear combination of independent univariate Lévy processes and can easily be calibratedto a set of one-dimensional marginal distributions and a given linear correlation matrix. Wederive conditions for our formulation and the associated calibration procedure to be well definedand provide some examples associated with particular Lévy processes permitting closedform characteristic function. Numerical results of the option premiums on three currenciesare presented to illustrate the effectiveness of our formulation with different linear correlationstructures.