Title: Calibration for Weak Variance-Alpha-Gamma Processes,
Abstract: The weak variance-alpha-gamma process is a multivariate Lévy process
constructed by weakly subordinating Brownian motion, possibly with correlated
components with an alpha-gamma subordinator. It generalises the
variance-alpha-gamma process of Semeraro constructed by traditional
subordination. We compare three calibration methods for the weak
variance-alpha-gamma process, method of moments, maximum likelihood estimation
(MLE) and digital moment estimation (DME). We derive a condition for Fourier
invertibility needed to apply MLE and show in our simulations that MLE produces
a better fit when this condition holds, while DME produces a better fit when it
is violated. We also find that the weak variance-alpha-gamma process exhibits a
wider range of dependence and produces a significantly better fit than the
variance-alpha-gamma process on an S&P500-FTSE100 data set, and that DME
produces the best fit in this situation.