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Calibration for Weak Variance-Alpha-Gamma Processes |
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| Authors: | Buchmann Boris Lu Kevin W Madan Dilip B |
| Institution: | 1.Research School of Finance, Actuarial Studies & Statistics, Australian National University, ACT, 0200, Australia ;2.Mathematical Sciences Institute, Australian National University, ACT, 0200, Australia ;3.Robert H. Smith School of Business, University of Maryland, College Park, MD, 20742, USA ; |
| 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 a S&P500-FTSE100 data set, and that DME produces the best fit in this situation. |
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