Calibration for Weak Variance-Alpha-Gamma Processes

Boris Buchmann; Kevin W. Lu; Dilip B. Madan

doi:10.1007/s11009-018-9655-y

Calibration for Weak Variance-Alpha-Gamma Processes

Boris Buchmann, Kevin W. Lu^*, Dilip B. Madan

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

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.

Original language	English
Pages (from-to)	1151-1164
Number of pages	14
Journal	Methodology and Computing in Applied Probability
Volume	21
Issue number	4
DOIs	https://doi.org/10.1007/s11009-018-9655-y
Publication status	Published - 1 Dec 2019

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10.1007/s11009-018-9655-y

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title = "Calibration for Weak Variance-Alpha-Gamma Processes",

abstract = "The weak variance-alpha-gamma process is a multivariate L{\'e}vy 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, Digital moment estimation, Gamma process, Log-Return, L{\'e}vy process, Maximum likelihood estimation, Method of moments, Self-Decomposability, Subordination, Variance-Alpha-Gamma, Variance-Gamma",

author = "Boris Buchmann and Lu, {Kevin W.} and Madan, {Dilip B.}",

note = "Publisher Copyright: {\textcopyright} 2018, Springer Science+Business Media, LLC, part of Springer Nature.",

year = "2019",

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doi = "10.1007/s11009-018-9655-y",

language = "English",

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T1 - Calibration for Weak Variance-Alpha-Gamma Processes

AU - Buchmann, Boris

AU - Lu, Kevin W.

AU - Madan, Dilip B.

PY - 2019/12/1

Y1 - 2019/12/1

N2 - 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.

AB - 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.

KW - Brownian motion

KW - Digital moment estimation

KW - Gamma process

KW - Log-Return

KW - Lévy process

KW - Maximum likelihood estimation

KW - Method of moments

KW - Self-Decomposability

KW - Subordination

KW - Variance-Alpha-Gamma

KW - Variance-Gamma

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U2 - 10.1007/s11009-018-9655-y

DO - 10.1007/s11009-018-9655-y

M3 - Article

SN - 1387-5841

VL - 21

SP - 1151

EP - 1164

JO - Methodology and Computing in Applied Probability

JF - Methodology and Computing in Applied Probability

IS - 4

ER -

Calibration for Weak Variance-Alpha-Gamma Processes

Abstract

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