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

Bibbona, Enrico; Sacerdote, Laura; Torre, Emiliano

doi:10.1007/s11009-016-9487-6

Cited by 7 publications

(3 citation statements)

References 41 publications

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“…• φ is the density function of a standard normal random variable. Bibbona et al [24] made use of ( 8) in their equations ( 24) and ( 26) to determine the copula for the Ornstein-Uhlenbeck process without mentioning that these equations had previously been developed by Schmitz [23]. Cherubini and Romagnoli [25] expressed (7) in the following conventional form of a Gaussian copula:…”

Section: Copulas and Brownian Motion: Foundation And Classical Resultsmentioning

confidence: 99%

A Class of Copulas Associated with Brownian Motion Processes and Their Maxima

Adès¹,

Dufour²,

Provost³

et al. 2022

JAMC

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The copulas being introduced in this paper are derived from distributions associated with the Brownian motion and related processes. Useful background information is initially presented. Attention is focused on univariate Brownian motion processes having a drift parameter and their running maxima as well as correlated bivariate Brownian motion processes in conjunction with the cumulative maxima of one of their components. The copulas generated therefrom as well as the corresponding density functions are explicitly provided and graphically represented. The derivations are thorough, with the requisite preliminary results being stated beforehand. As well, various potential applications are suggested. A numerical example involving an actual data set consisting of daily stock prices is worked out in detail. The associated empirical copula density function is determined in terms of Bernstein's polynomials and compared to one of our proposed theoretical copula densities. The steps that are provided, including an initial transformation of the observations which likens them to a Wiener process, should enable one to efficiently apply the novel results introduced herein to data sets arising in other areas.

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Section: Copulas and Brownian Motion: Foundation And Classical Resultsmentioning

confidence: 99%

A Class of Copulas Associated with Brownian Motion Processes and Their Maxima

Adès¹,

Dufour²,

Provost³

et al. 2022

JAMC

View full text Add to dashboard Cite

show abstract

“…In addition, our framework accommodates also Markov copulas, introduced in Darsow et al (1992) and developed also, for example, in Lagerås (2010), Ibragimov and Lentzas (2017), Ibragimov (2009), and Bibbona et al (2016), copulas for time series introduced in Cherubini et al (2012) and copulas in Hilbert spaces from Hausenblas and Riedle (2017).…”

Section: Copulas and Sklar's Theorem In Infinite Dimensionsmentioning

confidence: 99%

Copula measures and Sklar's theorem in arbitrary dimensions

Benth

Nunno

Schroers

2021

Scandinavian J Statistics

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Although copulas are used and defined for various infinite-dimensional objects (e.g., Gaussian processes and Markov processes), there is no prevalent notion of a copula that unifies these concepts. We propose a unified functional analytic framework, show how Sklar's theorem can be applied in certain examples of Banach spaces and provide a semiparametric estimation procedure for second-order stochastic processes with underlying Gaussian copula.

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“…, X tn ). The research in this direction was originated by seminal paper of Darsow, Nguyen and Olsen [7] and continued by many authors, amongst others Sempi [26], Bibbona et al [2] and Schmitz [23]. The second one concerns the vector valued stochastic processes X t = (X t , .…”

Section: Introductionmentioning

confidence: 99%

On Copula-Itô processes

Jaworski

2019

Dependence Modeling

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We study the dynamics of the family of copulas {Ct}t≥0 of a pair of stochastic processes given by stochastic differential equations (SDE). We associate to it a parabolic partial differential equation (PDE). Having embedded the set of bivariate copulas in a dual of a Sobolev Hilbert space H1 (ℝ2)* we calculate the derivative with respect to t and the *weak topology i.e. the tangent vector field to the image of the curve t → Ct. Furthermore we show that the family {Ct}t≥0 is an orbit of a strongly continuous semigroup of transformations and provide the infinitesimal generator of this semigroup.

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

Cited by 7 publications

References 41 publications

A Class of Copulas Associated with Brownian Motion Processes and Their Maxima

A Class of Copulas Associated with Brownian Motion Processes and Their Maxima

Copula measures and Sklar's theorem in arbitrary dimensions

On Copula-Itô processes

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