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A Copula-Based Method to Build Diffusion Models with Prescribed Marginal and Serial Dependence

Author

Listed:
  • Enrico Bibbona

    (University of Torino
    Politecnico di Torino)

  • Laura Sacerdote

    (University of Torino)

  • Emiliano Torre

    (Jülich Research Centre)

Abstract

This paper investigates the probabilistic properties that determine the existence of space-time transformations between diffusion processes. We prove that two diffusions are related by a monotone space-time transformation if and only if they share the same serial dependence. The serial dependence of a diffusion process is studied by means of its copula density and the effect of monotone and non-monotone space-time transformations on the copula density is discussed. This approach provides a methodology to build diffusion models by freely combining prescribed marginal behaviors and temporal dependence structures. Explicit expressions of copula densities are provided for tractable models.

Suggested Citation

  • Enrico Bibbona & Laura Sacerdote & Emiliano Torre, 2016. "A Copula-Based Method to Build Diffusion Models with Prescribed Marginal and Serial Dependence," Methodology and Computing in Applied Probability, Springer, vol. 18(3), pages 765-783, September.
    • Handle: RePEc:spr:metcap:v:18:y:2016:i:3:d:10.1007_s11009-016-9487-6
    DOI: 10.1007/s11009-016-9487-6
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    References listed on IDEAS

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    Cited by:

    1. Jaworski Piotr, 2019. "On Copula-Itô processes," Dependence Modeling, De Gruyter, vol. 7(1), pages 322-347, January.
    2. Fred Espen Benth & Giulia Di Nunno & Dennis Schroers, 2022. "Copula measures and Sklar's theorem in arbitrary dimensions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(3), pages 1144-1183, September.
    3. Fang, Jun & Jiang, Fan & Liu, Yong & Yang, Jingping, 2020. "Copula-based Markov process," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 166-187.

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