The Multivariate Variance Gamma Process and Its Applications in Multi-asset Option Pricing
Madan, Dilip B
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Dependence modeling plays a critical role in pricing and hedging multi-asset derivatives and managing risks with a portfolio of assets. With the emerge of structured products, it has attracted considerable interest in using multivariate Levy processes to model the joint dynamics of multiple financial assets. The traditional multidimensional extension assumes a common time change for each marginal process, which implies limited dependence structure and similar kurtosis on each marginal. In this thesis, we introduce a new multivariate variance gamma process which allows arbitrary marginal variance gamma (VG) processes with flexible dependence structure. Compared with other multivariate Levy processes recently proposed in the literature, this model has several advantages when applied to financial modeling. First, the multivariate process built with any marginal VG process is easy to simulate and estimate. Second, it has a closed form joint characteristic function which largely simplifies the computation problem of pricing multi-asset options. Last, it can be applied to other time changed Levy processes such as normal inverse Gaussian (NIG) process. To test whether the multivariate variance gamma model fits the joint distribution of financial returns, we compare the model performance of explaining the portfolio returns with other popular models and we also develop Fast Fourier Transform (FFT)-based methods in pricing multi-asset options such as exchange options, basket options and cross-currency foreign exchange options.