- Article

Ñíguez, T.M. and Perote, J. 2011. A New Proposal for Computing Portfolio Value-at-Risk for Semi-nonparametric Distributions. *International Journal of Mathematics and Computers in Simulation .* 5 (2), pp. 85-92.

Title | A New Proposal for Computing Portfolio Value-at-Risk for Semi-nonparametric Distributions |
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Authors | Ñíguez, T.M. and Perote, J. |

Abstract | This paper proposes a semi-nonparametric (SNP) methodology for computing portfolio value-at-risk (VaR) that is more accurate than both the traditional Gaussian-assumption-based methods implemented in the software packages used by risk analysts (RiskMetrics), and alternative heavy-tailed distributions that seem to be very rigid to incorporate jumps and asymmetries in the distribution tails (e.g. the Student’s t). The outperformance of the SNP distributions lies in the fact that Edgeworth and Gram-Charlier series represent a valid asymptotic approximation of any “regular” probability density function. In fact these expansions involve general and flexible parametric representations capable of featuring the salient empirical regularities of financial data. Furthermore these distributions can be extended to a multivariate context and may be estimated in several steps and thus we propose to estimate portfolio VaR in three steps: Firstly, estimating the conditional variance and covariance matrix of the portfolio consistently with the multivariate SNP distribution; Secondly, estimating the univariate distribution of the portfolio constrained to the portfolio variance obtained from the previous step; Thirdly, computing the corresponding quantile of the portfolio distribution by implementing straightforward recursive algorithms. We estimate the VaRs obtained with such methodology for different bivariate portfolios of stock indices and interests rates finding a clear underestimation (overestimation) of VaR measures obtained from the traditional Gaussian- (Student’s t-) based methods compared to our SNP approach. |

Keywords | Edgeworth and Gram-Charlier series, GARCH models, multivariate densities, semi-nonparametric distributions, Value-at-Risk. |

Journal | International Journal of Mathematics and Computers in Simulation |

Journal citation | 5 (2), pp. 85-92 |

ISSN | 1998-0159 |

Year | 2011 |

Publisher | North Atlantic University Union NAUN |

Publisher's version | Ñíguez.pdf |

Web address (URL) | http://www.naun.org/main/NAUN/mcs/19-839.pdf |

Publication dates | |

Published | 2011 |

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Ñíguez, T.M., Paya, I., Peel, D. and Perote, J. 2015. Higher-Order Risk Preferences, Constant Relative Risk Aversion and the Optimal Portfolio Allocation. *Bank of Spain Working Paper Series.* 1520.

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Ñíguez, T.M., Paya, I., Peel, D. and Perote, J. 2014. Higher-order moments in the theory of diversifying and portfolio composition. *XXII Annual Symposium of the Society of Nonlinear Dynamics and Econometrics .* New York, USA. Apr 2014

Higher-order Moments in the Theory of Diversification and Portfolio Composition

Ñíguez, T.M., Paya, I., Peel, D. and Perote, J. 2014. Higher-order Moments in the Theory of Diversification and Portfolio Composition. *XV Conference on International Economics, Spanish Association of International Economics and Finance.* Salamanca, Spain. May 2014

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Ñíguez, T.M. and Perote, J. 2014. The Moments Expansion Density. *10th BMRC-DEMS Conference.* Brunel University, London, UK. May 2014

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Ñíguez, T.M. and Perote, J. 2014. The Multivariate Moments Expansion Density: An Application of the Dynamic Equicorrelation Model. *Annual International Finance and Banking Conference, International Finance and Banking Society.* Lisbon, Portugal. Jun 2014

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Multivariate Semi-nonparametric Distributions with Dynamic Conditional Correlations

Del Brio, E.B., Ñíguez, T.M. and Perote, J. 2011. Multivariate Semi-nonparametric Distributions with Dynamic Conditional Correlations. *International Journal of Forecasting.* 27 (2), pp. 347-364. doi:10.1016/j.ijforecast.2010.02.005

Multivariate distributions based on general moments expansions: evidence from exchange rates

Ñíguez, T.M., Perote, J. and Rubia, A. 2011. Multivariate distributions based on general moments expansions: evidence from exchange rates. *4th workshop in risk management and insurance.* Seville, Spain. October 2011

Multivariate distributions based on general moments expansions: evidence from exchange rates

Ñíguez, T.M., Perote, J. and Rubia, A. 2011. Multivariate distributions based on general moments expansions: evidence from exchange rates. *European financial management association annual conference.* Braga, Portugal. June 2011

Multivariate distributions based on general moments expansions: evidence from exchange rates

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Ñíguez, T.M., Perote, J. and Rubia, A. 2011. Multivariate distributions based on general moments expansions: evidence from exchange rates. *Workshop in time series econometrics.* Zaragoza, Spain. April 2011

On the stability of the CRRA utility under high degrees of uncertainty

Ñíguez, T.M., Paya, I., Peel, D. and Perote, J. 2011. *On the stability of the CRRA utility under high degrees of uncertainty.* Lancaster University Management School.

Forecasting the unconditional and conditional kurtosis of the asset returns distribution

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Gram-Charlier Densities: A Multivariate Approach

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Multivariate semi-nonparametric densities with dynamic conditional correlations

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The general moments expansion and its applications for financial risk

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Ñíguez, T.M. 2008. *Predicting the monthly volatility of the EuroStoxx 50 Index using data sampled at different frequencies. Macroeconomic forecast and analysis laboratory discussion paper.* Institute Flores de Lemus, Carlos III University of Madrid.

Multivariate Gram-Charlier densities

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Semi-parametric density expansions: orthogonality vs simplicity

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Multivariate Gram-Charlier densities

Del Brio, E.B., Ñíguez, T.M. and Perote, J. 2007. Multivariate Gram-Charlier densities. *1st International Workshop on Computational and Financial Econometrics.* Geneva, Switzerland. Apr 2007

Multivariate Gram-Charlier densities

Del Brio, E.B., Ñíguez, T.M. and Perote, J. 2007. Multivariate Gram-Charlier densities. *Annual Meeting of the Journal of Financial Econometrics.* Faro, Portugal. Oct 2007

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Forecasting heavy-tailed densities with positive Edgeworth-Sargan and Gram-Charlier expansion

Perote, J. and Ñíguez, T.M. 2006. Forecasting heavy-tailed densities with positive Edgeworth-Sargan and Gram-Charlier expansion. *XXVI International Symposium of Forecasting.* Santander, Spain. Jun 2006

Forecasting heavy-tailed densities with positive Edgeworth-Sargan and Gram-Charlier expansion

Perote, J. and Ñíguez, T.M. 2005. Forecasting heavy-tailed densities with positive Edgeworth-Sargan and Gram-Charlier expansion. *XIII Forum of Finance.* Madrid, Spain. Nov 2005

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Forecasting heavy-tailed densities with positive Edgeworth and Gram-Charlier expansions

Ñíguez, T.M. and Perote, J. 2005. Forecasting heavy-tailed densities with positive Edgeworth and Gram-Charlier expansions. *XXX Symposium of the Economic Analysis.* Murcia, Spain Dec 2005

Estimating the dynamics of interest rates in the Japanese economy

Ñíguez, T.M. and Nowman, K.B. 2005. Estimating the dynamics of interest rates in the Japanese economy. *Westminster Business School Workshop in Memory of the Late Professor Albert Rex Bergstrom on Continuous Time Econometrics.* London, UK. Dec 2005

Forecasting the density of asset returns

Ñíguez, T.M. and Perote, J. 2004. *Forecasting the density of asset returns.* London, UK London School of Economics and Political Science.

Forecasting the conditional covariance matrix of a portfolio under long-run temporal dependence

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Forecasting the conditional covariance matrices of a portfolio under long-run temporal dependence

Ñíguez, T.M. and Rubia, A. 2002. Forecasting the conditional covariance matrices of a portfolio under long-run temporal dependence. *Instituto Valenciano de Investigaciones Economicas.* Seville, Spain. Oct 2002

Volatility and VaR forecasting for the IBEX-35 stock-return index using FIGARCH-type processes and different evaluation criteria

Ñíguez, T.M. 2002. Volatility and VaR forecasting for the IBEX-35 stock-return index using FIGARCH-type processes and different evaluation criteria. *XXVII Symposium of the Economic Analysis.* Salamanca, Spain. Dec 2002

Forecasting the conditional covariance matrix of a portfolio under long-run temporal dependence

Ñíguez, T.M. 2002. Forecasting the conditional covariance matrix of a portfolio under long-run temporal dependence. *XXVII Symposium of the Economic Analysis.* Salamanca, Spain. Dec 2002

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