Calibration for Weak Variance-Alpha-Gamma Processes

Boris Buchmann (), Kevin W. Lu () and Dilip B. Madan ()
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Boris Buchmann: Australian National University
Kevin W. Lu: Australian National University
Dilip B. Madan: University of Maryland

Methodology and Computing in Applied Probability, 2019, vol. 21, issue 4, 1151-1164

Abstract: 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.

Keywords: Brownian motion; Gamma process; Lévy process; Subordination; Variance-Gamma; Variance-Alpha-Gamma; Self-Decomposability; Log-Return; Method of moments; Maximum likelihood estimation; Digital moment estimation; Primary: 60G51; Secondary: 62F10; 60E10 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s11009-018-9655-y

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