A multivariate Levy process model with linear correlation
In this paper, we develop a multivariate risk-neutral Levy process model and discuss its applicability in the context of the volatility smile of multiple assets. Our formulation is based upon a linear combination of independent univariate Levy processes and can easily be calibrated to a set of one-dimensional marginal distributions and a given linear correlation matrix. We derive conditions for our formulation and the associated calibration procedure to be well-defined and provide some examples associated with particular Levy processes permitting a closed-form characteristic function. Numerical results of the option premiums on three currencies are presented to illustrate the effectiveness of our formulation with different linear correlation structures.
Volatility modelling, Stochastic jumps, Non-Gaussian option pricing, Non-Gaussian distributions, Multivariate volatility, Model calibration, Mathematical finance, Implementation of pricing,
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