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

Enrico Bibbona (), Laura Sacerdote () and Emiliano Torre ()
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Enrico Bibbona: University of Torino
Laura Sacerdote: University of Torino
Emiliano Torre: Jülich Research Centre

Methodology and Computing in Applied Probability, 2016, vol. 18, issue 3, 765-783

Abstract: 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.

Keywords: Copulae; Copulas; Space-time transformations; Diffusions; Serial dependence; Stochastic differential equations; 60J60; 62M10 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s11009-016-9487-6

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