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Marginal consistent dependence modelling using weak subordination for Brownian motions

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  • Markus Michaelsen
  • Alexander Szimayer

Abstract

We present an approach for modelling dependencies in exponential Lévy market models with arbitrary margins originated from time changed Brownian motions. Using weak subordination of Buchmann et al. [Bernoulli, 2017], we face a new layer of dependencies, superior to traditional approaches based on pathwise subordination, since weakly subordinated processes are not required to have independent components considering multivariate stochastic time changes. We apply a subordinator being able to incorporate any joint or idiosyncratic information arrivals. We emphasize multivariate variance gamma and normal inverse Gaussian processes and state explicit formulae for the Lévy characteristics. Using maximum likelihood, we estimate multivariate variance gamma models on various market data and show that these models are highly preferable to traditional approaches. Consistent values of basket-options under given marginal pricing models are achieved using the Esscher transform, generating a non-flat implied correlation surface.

Suggested Citation

  • Markus Michaelsen & Alexander Szimayer, 2018. "Marginal consistent dependence modelling using weak subordination for Brownian motions," Quantitative Finance, Taylor & Francis Journals, vol. 18(11), pages 1909-1925, November.
    • Handle: RePEc:taf:quantf:v:18:y:2018:i:11:p:1909-1925
    DOI: 10.1080/14697688.2018.1439182
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    Citations

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    Cited by:

    1. 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.
    2. M. Gardini & P. Sabino & E. Sasso, 2021. "The Variance Gamma++ Process and Applications to Energy Markets," Papers 2106.15452, arXiv.org.
    3. Matteo Gardini & Piergiacomo Sabino, 2022. "Exchange option pricing under variance gamma-like models," Papers 2207.00453, arXiv.org.
    4. Tim Leung & Kevin W. Lu, 2023. "Monte Carlo Simulation for Trading Under a L\'evy-Driven Mean-Reverting Framework," Papers 2309.05512, arXiv.org, revised Jan 2024.
    5. 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.
    6. Buchmann, Boris & Lu, Kevin W. & Madan, Dilip B., 2020. "Self-decomposability of weak variance generalised gamma convolutions," Stochastic Processes and their Applications, Elsevier, vol. 130(2), pages 630-655.
    7. Michele Leonardo Bianchi & Asmerilda Hitaj & Gian Luca Tassinari, 2020. "Multivariate non-Gaussian models for financial applications," Papers 2005.06390, arXiv.org.
    8. Matteo Gardini & Piergiacomo Sabino & Emanuela Sasso, 2021. "Correlating Lévy processes with self-decomposability: applications to energy markets," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(2), pages 1253-1280, December.
    9. Hersugondo Hersugondo & Endang Tri Widyarti & Di Asih I Maruddani & Trimono Trimono, 2022. "ASEAN-5 Stock Price Index Valuation after COVID-19 Outbreak through GBM-MCS and VaR-SDPP Methods," IJFS, MDPI, vol. 10(4), pages 1-19, November.

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