Buchmann, BorisLu, KevinMadan, Dilip B.2021-06-09Buchmann, B., Lu, K.W. & Madan, D.B. Calibration for Weak Variance-Alpha-Gamma Processes. Methodol Comput Appl Probab 21, 1151–1164 (2019). https://doi.org/10.1007/s11009-018-9655-y1387-5841http://hdl.handle.net/1885/236910The 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 a S&P500-FTSE100 data set, and that DME produces the best fit in this situation.B. Buchmann's research was supported by ARC grant DP160104737. K. Lu's research was supported by an Australian Government Research Training Program Scholarship.application/pdfen-AU© 2018 Springer Science+Business Media, LLC, part of Springer NatureBrownian motionGamma processLevy processSubordinationVariance-GammaVariance-Alpha-GammaSelf-DecomposabilityLog-ReturnMethod of momentsMaximum likelihood estimationDigital moment estimation2018-08-2310.1007/s11009-018-9655-y