Calibration for Weak Variance-Alpha-Gamma Processes
Date
2018-08-23
Authors
Buchmann, Boris
Lu, Kevin
Madan, Dilip B.
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Volume Title
Publisher
Kluwer Academic Publishers
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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Keywords
Brownian motion, Gamma process, Levy process, Subordination, Variance-Gamma, Variance-Alpha-Gamma, Self-Decomposability, Log-Return, Method of moments, Maximum likelihood estimation, Digital moment estimation
Citation
Buchmann, 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-y
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Source
Methodology and Computing in Applied Probability
Type
Journal article
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Open Access
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Author accepted manuscript