Using Conditional Copula to Estimate Value at Risk

Palaro, Helder P.; Hotta, Luiz Koodi

doi:10.2139/ssrn.818884

Cited by 22 publications

(28 citation statements)

References 28 publications

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“…Overall, the time-varying DCC t-copula improves traditional portfolio optimization models by accounting for nonlinearities in the dependence between portfolio's assets and dynamic changes of the dependence structure. Additionally, we are able to achieve VaR figures, based on the calibrated DCC t-copula by simulating N observations characterized by the DCC t-copula dependence structure (Palaro and Hotta, 2006). Following Berger (2013), we simulate 10,000 observations for each day and the LVaR is determined by the empirical quantile.…”

Section: • + Mn=mentioning

confidence: 99%

Multivariate dependence and portfolio optimization algorithms under illiquid market scenarios

Janabi

Hernández

Berger

et al. 2017

European Journal of Operational Research

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We propose a model for optimizing structured portfolios with liquidity-adjusted Value-at-Risk (LVaR) constraints, whereby linear correlations between assets are replaced by the multivariate nonlinear dependence structure based on Dynamic Conditional Correlation t-copula modeling. Our portfolio optimization algorithm minimizes the LVaR function under adverse market circumstances and multiple operational and financial constraints. When we consider a diversified portfolio of international stock and commodity market indices under multiple realistic portfolio optimization scenarios, the obtained results consistently show the superiority of our approach relative to other competing portfolio strategies including the minimum-variance, risk-parity and equally weighted portfolio allocations.

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Section: • + Mn=mentioning

confidence: 99%

Multivariate dependence and portfolio optimization algorithms under illiquid market scenarios

Janabi

Hernández

Berger

et al. 2017

European Journal of Operational Research

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“…We denote the log-returns of Nasdaq as variable 1 (X, say) and the log-returns of S&P 500 as variable 2 (Y). For details on this data set, see Palaro and Hotta (2006).…”

Section: Application In Risk Managementmentioning

confidence: 99%

“…In order to specify the bivariate model for these two returns, and to estimate the associated Var under several bivariate copula models, we will consider some specific Autoregressive integrated moving average-Generalized Autoregressive Conditional Heteroskedastic (or in short, ARMA-GARCH) models, the reason being that return series are usually successfully modeled by ARMA-GARCH models by many authors. As suggested in Palaro and Hotta (2006), we will mainly consider three different ARMA-GARCH models: GARCH-N, GARCH-t, and GARCH-E. In terms of modeling the dependence between the two series, we consider three copula functions that are quite popular among other authors: FGM, Gumbel-Hougaard, Bivariate Gaussian copula along with our bivariate KW-FGM type copulas.…”

Section: Application In Risk Managementmentioning

confidence: 99%

“…In terms of modeling the dependence between the two series, we consider three copula functions that are quite popular among other authors: FGM, Gumbel-Hougaard, Bivariate Gaussian copula along with our bivariate KW-FGM type copulas. In order to asses the accuracy of the VaR estimates at 95%, and 99% confidence level, we followed the procedure as discussed in Palaro and Hotta (2006). In the table below, we present the proportion of observations (in brackets), for t = 751 to 2971, where the portfolio loss exceeded the estimated VaR for α = 0.05.…”

Section: Application In Risk Managementmentioning

confidence: 99%

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Bivariate Kumaraswamy Models via Modified FGM Copulas: Properties and Applications

Ghosh

2017

JRFM

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A copula is a useful tool for constructing bivariate and/or multivariate distributions. In this article, we consider a new modified class of FGM (Farlie-Gumbel-Morgenstern) bivariate copula for constructing several different bivariate Kumaraswamy type copulas and discuss their structural properties, including dependence structures. It is established that construction of bivariate distributions by this method allows for greater flexibility in the values of Spearman's correlation coefficient, ρ and Kendall's τ.

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“…Compared with traditional methods of Value at Risk (VaR) estimation, conditional copula theory can be a very powerful tool in estimating the VaR, as shown by [27] and [46]. However, modeling high-dimensional distributions is not an easy task and only a few models are potentially useful for constructing exible distribution models in high dimensions.…”

Section: Introductionmentioning

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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Using Conditional Copula to Estimate Value at Risk

Cited by 22 publications

References 28 publications

Multivariate dependence and portfolio optimization algorithms under illiquid market scenarios

Multivariate dependence and portfolio optimization algorithms under illiquid market scenarios

Bivariate Kumaraswamy Models via Modified FGM Copulas: Properties and Applications

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

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