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Calibration for Weak Variance-Alpha-Gamma Processes

Author

Listed:
  • Boris Buchmann

    (Australian National University)

  • Kevin W. Lu

    (Australian National University)

  • Dilip B. Madan

    (University of Maryland)

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.

Suggested Citation

  • Boris Buchmann & Kevin W. Lu & Dilip B. Madan, 2019. "Calibration for Weak Variance-Alpha-Gamma Processes," Methodology and Computing in Applied Probability, Springer, vol. 21(4), pages 1151-1164, December.
    • Handle: RePEc:spr:metcap:v:21:y:2019:i:4:d:10.1007_s11009-018-9655-y
    DOI: 10.1007/s11009-018-9655-y
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    References listed on IDEAS

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    Cited by:

    1. Matteo Gardini & Edoardo Santilli, 2023. "A Heath-Jarrow-Morton framework for energy markets: a pragmatic approach," Papers 2305.01485, arXiv.org, revised Nov 2023.
    2. M. Gardini & P. Sabino & E. Sasso, 2021. "The Variance Gamma++ Process and Applications to Energy Markets," Papers 2106.15452, arXiv.org.
    3. Kevin W. Lu, 2022. "Calibration for multivariate Lévy-driven Ornstein-Uhlenbeck processes with applications to weak subordination," Statistical Inference for Stochastic Processes, Springer, vol. 25(2), pages 365-396, July.
    4. Michele Leonardo Bianchi & Asmerilda Hitaj & Gian Luca Tassinari, 2020. "Multivariate non-Gaussian models for financial applications," Papers 2005.06390, arXiv.org.

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