Copulas for Finance - A Reading Guide and Some Applications

Bouyé, Éric; Nikeghbali, Ashkan; Roncalli, Thierry

doi:10.2139/ssrn.1032533

Cited by 308 publications

(189 citation statements)

References 50 publications

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“…Consequently the model that is used for dependence is of key importance for portfolio management and portfolio selection. In this section we use the tests of the previous section to choose among the Gaussian, the Student's t, and the 9 Simulation techniques for copulas can be found in Bouyé et al (2000) and Cherubini et al (2004), Ch. 6.…”

Section: Applying Copulas In Risk Managementmentioning

confidence: 99%

Selecting copulas for risk management

Kole

Koedijk

Verbeek

2007

Journal of Banking & Finance

255

120

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Copulas offer financial risk managers a powerful tool to model the dependence between the different elements of a portfolio and are preferable to the traditional, correlation-based approach. In this paper we show the importance of selecting an accurate copula for risk management. We extend standard goodness-of-fit tests to copulas. Contrary to existing, indirect tests, these tests can be applied to any copula of any dimension and are based on a direct comparison of a given copula with observed data. For a portfolio consisting of stocks, bonds and real estate, these tests provide clear evidence in favor of the Student's t copula, and reject both the correlation-based Gaussian copula and the extreme value-based Gumbel copula. In comparison with the Student's t copula, we find that the Gaussian copula underestimates the probability of joint extreme downward movements, while the Gumbel copula overestimates this risk. Similarly we establish that the Gaussian copula is too optimistic on diversification benefits, while the Gumbel copula is too pessimistic. Moreover, these differences are significant.

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Section: Applying Copulas In Risk Managementmentioning

confidence: 99%

Selecting copulas for risk management

Kole

Koedijk

Verbeek

2007

Journal of Banking & Finance

255

120

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“…We can maximize an objective function that approximates the pro le log-likelihood for the degrees of freedom parameter as in [9] with the following algorithm:…”

Section: DCC T-copulamentioning

confidence: 99%

Large portfolio risk management and optimal portfolio allocation with dynamic elliptical copulas

Jin

Lehnert

2018

Dependence Modeling

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Previous research has focused on the importance of modeling the multivariate distribution for optimal portfolio allocation and active risk management. However, existing dynamic models are not easily applied to high-dimensional problems due to the curse of dimensionality. In this paper, we extend the framework of the Dynamic Conditional Correlation/Equicorrelation and an extreme value approach into a series of Dynamic Conditional Elliptical Copulas. We investigate risk measures such as Value at Risk (VaR) and Expected Shortfall (ES) for passive portfolios and dynamic optimal portfolios using Mean-Variance and ES criteria for a sample of US stocks over a period of 10 years. Our results suggest that (1) Modeling the marginal distribution is important for dynamic high-dimensional multivariate models. (2) Neglecting the dynamic dependence in the copula causes over-aggressive risk management. (3) The DCC/DECO Gaussian copula and t-copula work very well for both VaR and ES. (4) Grouped t-copulas and t-copulas with dynamic degrees of freedom further match the fat tail. (5) Correctly modeling the dependence structure makes an improvement in portfolio optimization with respect to tail risk. (6) Models driven by multivariate t innovations with exogenously given degrees of freedom provide a exible and applicable alternative for optimal portfolio risk management.

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“…Evaluation of ϑ can be carried out by using the Canonical Maximum Likelihood (CML) method [14][15][16][17]. After parameter estimation, the choice of the copula function that best fits the sample can be made by considering the following C-measure, named as Kendall function [16,18,19]:…”

Section: Overview Of Copula Functionsmentioning

confidence: 99%

Bivariate Return Period for Design Hyetograph and Relationship with T-Year Design Flood Peak

Luca

Biondi

2017

Water

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This study focuses on the return period evaluation for design hyetographs, which is usually estimated by adopting a univariate statistical approach. Joint Return Period (JRP) and copula-based multivariate analysis are used in this work to better define T-year synthetic rainfall patterns which can be used as input for design flood peak estimation by means of hydrological simulation involving rainfall-runoff (RR) models. Specifically, a T-year Design Hyetograph (DH) is assumed to be characterized by its peak H, at the chosen time resolution ∆t, and by the total rainfall height W, cumulated on its critical duration d Crit , which has been a priori fixed. As stated in technical literature, the choice of the expression for JRP depends on which event is deemed as critical for the investigated system; the most important cases are: (i) all the variables must exceed a certain magnitude to achieve critical conditions; or (ii) at least one variable must be greater than a threshold; or (iii) critical conditions are induced by all the events with a joint Cumulative Density Function (CDF) overcoming an assigned probability threshold. Once the expression for JRP was chosen, the relationship among multivariate T-year design hyetographs and T-year design flood peak was investigated for a basin located in Calabria region (southern Italy). Specifically, for the selected case study, a summary diagram was obtained as final result, which allows the main characteristics of T-year DHs to be estimated, considering both the univariate and the copula based multivariate analysis, and the associated T-year design flood peaks obtained through the simulation with a RR model.

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Copulas for Finance - A Reading Guide and Some Applications

Cited by 308 publications

References 50 publications

Selecting copulas for risk management

Selecting copulas for risk management

Large portfolio risk management and optimal portfolio allocation with dynamic elliptical copulas

Bivariate Return Period for Design Hyetograph and Relationship with T-Year Design Flood Peak

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