VOLATILITY AND VAR FORECASTING FOR THE IBEX-35 STOCK-RETURN INDEX USING FIGARCH-TYPE PROCESSES AND DIFFERENT EVALUATION CRITERIA

In this paper I analyze the relative performance of Gaussian and Student-t GARCH and FIGARCH type models for volatility and Value-at-Risk forecasting of daily stock-returns using data from the Spanish equity index IBEX-35. The in-sample analysis shows that the Student-t FIAPARCH process provides a better fit than the nested models. Regarding the out-of-sample volatility forecasting, both the Gaussian- and the t-FIAPARCH processes show the best performance, although it is not possible to discriminate between them. As for the models' capacity for VaR forecasting, different results are obtained according to the evaluation criteria considered, although if the aim is regulatory VaR it is shown that the Student-t FIAPARCH model would be clearly the most recommendable.APARCH, Fractional Integration, Leverage Effect, Long Memory, Value-at-risk

Forecasting the density of asset returns

In this paper we introduce a transformation of the Edgeworth-Sargan series expansion of the Gaussian distribution, that we call Positive Edgeworth-Sargan (PES). The main advantage of this new density is that it is well defined for all values in the parameter space, as well as it integrates up to one. We include an illustrative empirical application to compare its performance with other distributions, including the Gaussian and the Student's t, to forecast the full density of daily exchange-rate returns by using graphical procedures. Our results show that the proposed function outperforms the other two models for density forecasting, then providing more reliable value-at-risk forecasts.Density forecasting, Edgeworth-Sargan distribution, probability integral transformations, P-value plots, VaR

Predicting the monthly volatility of the EuroStoxx 50 using data sampled at different frequencies

This paper analyses the forecastability of the EuroStoxx 50 monthly returns volatil- ity. We consider different proxies for the unobserved volatility variable by using data sampled at di¤erent frequencies, and GARCH and AGARCH models with Normal and Student s t errors for the dynamics of returns conditional variance. We nd that a method based on aggregation of multi step (daily) ahead GARCH-type forecasts provide quite accurate predictions of monthly volatility

Backtesting VaR under the COVID-19 sudden changes in volatility

We analyze the impact of the COVID-19 pandemic on the conditional variance of stock returns. We look at this effect from a global perspective, so we employ series of major stock market and sector indices. We use the Hansen's Skewed-t distribution with EGARCH extended to control for sudden changes in volatility. We oversee the COVID-19 effect on measures of downside risk such as the Value-at-Risk. Our results show that there is a significant sudden shift up in the return distribution variance post the announcement of the pandemic, which must be explained properly to obtain reliable measures for financial risk management. [Abstract copyright: Crown Copyright © 2021 Published by Elsevier Inc. All rights reserved.

Multivariate Gram-Charlier Densities

This paper introduces a new family of multivariate distributions based on Gram-Charlier and Edgeworth expansions. This family encompasses many of the univariate seminonparametric densities proposed in the financial econometrics as marginal distributions of the different formulations. Within this family, we focus on the specifications that guarantee positivity so obtaining a well-defined multivariate density. We compare different "positive" multivariate distributions of the family with the multivariate Edgeworth-Sargan, Normal and Student’s t in an in- and out-sample framework for financial returns data. Our results show that the proposed specifications provide a quite reasonably good performance being so of interest for applications involving the modelling and forecasting of heavy-tailed distributions.Multivariate distributions; Gram-Charlier and Edgeworth-Sargan densities; MGARCH models; financial data

Multivariate moments expansion density : application of the dynamic equicorrelation model

En este estudio, proponemos un nuevo tipo de distribución semi-noparamétrica (SNP) para describir la densidad de los rendimientos de las carteras de activos. Esta distribución, denominada «expansión de momentos multivariante» (MME), admite cualquier distribución (multivariante) no-Gausiana como base de la expansión, ya que está directamente especificada en términos de los momentos de dicha distribución. En el caso de la expansión de una distribución normal, la MME es una reformulación de la distribución Gram-Charlier multivariante (MGC), pero, cuando se utilizan transformaciones de positividad para obtener densidades bien definidas, la MME es más sencilla y manejable que la MGC. Como aplicación empírica, extendemos el modelo de equicorrelación dinámica condicional (DECO) a un contexto SNP utilizando la MME. El modelo resultante presenta una formulación sencilla que admite la estimación consistente en dos etapas e incorpora DECO, así como las características no-Gausianas de la distribución de los rendimientos de cartera. La capacidad predictiva del modelo MME-DECO para una cartera de 10 activos demuestra que puede ser una herramienta útil para la gestión y el control del riesgo de carteraIn this study, we propose a new semi-nonparametric (SNP) density model for describing the density of portfolio returns. This distribution, which we refer to as the multivariate moments expansion (MME), admits any non-Gaussian (multivariate) distribution as its basis because it is specified directly in terms of the basis densitys moments. To obtain the expansion of the Gaussian density, the MME is a reformulation of the multivariate Gram-Charlier (MGC), but the MME is much simpler and tractable than the MGC when positive transformations are used to produce well-defined densities. As an empirical application, we extend the dynamic conditional equicorrelation (DECO) model to an SNP framework using the MME. The resulting model is parameterized in a feasible manner to admit two-stage consistent estimation, and it represents the DECO as well as the salient non-Gaussian features of portfolio return distributions. The in- and out-of-sample performance of a MME-DECO model of a portfolio of 10 assets demonstrates that it can be a useful tool for risk management purpose

Polynomial adjusted Student-t densities for modeling asset returns

We present a polynomial expansion of the standardized Student-t distribution. Our density, obtained through the polynomial adjusted method in Bagnato, Potí, and Zoia (2015. “The Role of Orthogonal Polynomials in Adjusting Hyperbolic Secant and Logistic Distributions to Analyse Financial Asset Returns.” Statistical Papers 56 (4): 1205–12340), is an extension of the Gram–Charlier density in Jondeau and Rockinger (2001. “Gram-Charlier Densities.” Journal of Economic Dynamics and Control 25 (10): 1457–1483). We derive the closed-form expressions of the moments, the distribution function and the skewness–kurtosis frontier for a well-defined density. An empirical application is also implemented for modeling heavy-tailed and skewed distributions for daily asset returns. Both in-sample and backtesting analysis show that this new density can be a good candidate for risk management.Financial support from the Spanish Ministry of Economy and Competitiveness through grant ECO2017-87069-P is gratefully acknowledged by Ángel León

Backtesting VaR under the COVID-19 sudden changes in volatility

We analyze the impact of the COVID-19 pandemic on the conditional variance of stock returns. We look at this effect from a global perspective, so we employ series of major stock market and sector indices. We use the Hansen’s Skewed-t distribution with EGARCH extended to control for sudden changes in volatility. We oversee the COVID-19 effect on measures of downside risk such as the Value-at-Risk. Our results show that there is a significant sudden shift up in the return distribution variance post the announcement of the pandemic, which must be explained properly to obtain reliable measures for financial risk management.Financial support from the Spanish Ministry of Economy and Competitiveness through grant ECO2017-87069-P is gratefully acknowledged by the second author

Higher-order risk preferences, constant relative risk aversion and the optimal portfolio allocation

Derivamos las condiciones para la elección óptima de cartera bajo una utilidad con aversión al riesgo relativo constante y distribuciones de probabilidad alternativas que son capaces de capturar las caraterísticas de asimetría y curtosis de los rendimientos de los activos financieros. Ilustramos el papel —más allá de la aversión al riesgo— que desempeñan los momentos de orden superior en la decisión de formar una cartera de activos. En particular, demostramos que las actitudes de orden superior, tales como la prudencia y la temperancia, asociadas a los momentos tercero y cuarto de la distribución, definen diferentes carteras óptimas a las restringidas bajo aversión al riesgoWe derive the conditions for the optimal portfolio choice within a constant relative risk aversion type of utility function considering alternative probability distributions that are able to capture the asymmetric and leptokurtic features of asset returns. We illustrate the role —beyond risk aversion— played by higher-order moments in the optimal decision to form a portfolio of risky assets. In particular, we show that higher-order risk attitudes such as prudence and temperance associated with the third and fourth moments of the distribution define different optimal portfolios than those constrained under risk aversio

Skewness in energy returns: Estimation, testing and implications for tail risk

In this paper we estimate the skewness of the unconditional distribution of energy returns and test its statistical significance. We compare the performance of traditional and robust tests for skewness with those based on the implied unconditional skewness in a TGARCH model with Gram-Charlier (TGARCH-GC) innovations. We also analyze the implications of TGARCH-GC skewness for tail risk through evaluation of Value-at-Risk (VaR) and expected shortfall (ES) accuracy. Our results show that crude oil (Brent and WTI) and Gasoline returns are negatively skewed, while we do not find evidence of skewed distribution for other energy returns such as Heating oil, Kerosene and Natural gas. This indicates that the returns of the former are likely to encapsulate more largely the effect of negative shocks and so present higher tail risk than those of the latter. These results differ from traditional and robust tests for skewness providing important information on how to improve mean-variance risk management measures. Indeed, we find that the three-moment VaR and ES measures based on the third-order Cornish Fisher (CF3) expansion for the unconditional distribution of returns considerably improve their corresponding two-moment ones. We adopt CF3 to disentangle skewness effects from kurtosis in tail risk.Financial support from the Spanish Government under project PID2021-124860NB-I00 and from the Generalitat Valenciana under project CIPROM/2021/060 is gratefully acknowledged