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South Africa s economy has faced many downturns in the previous decade, and to curb the spread of the novel SARS-CoV-2, the lockdown brought South African financial markets to an abrupt halt. Therefore, the implementation of risk mitigation approaches is becoming a matter of urgency in volatile markets in these unprecedented times. In this study, a hybrid generalized autoregressive conditional heteroscedasticity (GARCH)-Type model combined with heavy-Tailed distributions, namely the Generalized Pareto Distribution (GPD) and the Nolan s S0-parameterization stable distribution (SD), were fitted to the returns of three FTSE/JSE indices, namely All Share Index (ALSI), Banks Index and Mining Index, as well as the daily closing prices of the US dollar against the South African rand exchange rate (USD/ZAR exchange rate). VaR values were estimated and back-Tested using the Kupiec likelihood ratio test. The results of this study show that for FTSE/JSE ALSI returns, the hybrid exponential GARCH (1,1) model with SD model (EGARCH(1,1)-SD) outperforms the GARCHGPD model at the 2.5% VaR level. At VaR levels of 95% and 97.5%, the fitted GARCH (1,1)-SD model for FTSE/JSE Banks Index returns performs better than the GARCH (1,1)-GPD. The fitted GARCH (1,1)-SD model for FTSE/JSE Mining Index returns is better than the GARCH (1,1)-GPD at 5% and 97.5% VaR levels. Thus, this study suggests that the GARCH (1,1)-SD model is a good alternative to the VaR robust model for modeling financial returns. This study provides salient results for persons interested in reducing losses or obtaining a better understanding of the South African financial industry. © 2021 LLC CPC Business Perspectives. All rights reserved.

Whereas much research has largely investigated the safe haven, diversifier and hedge proprieties of cryptocurrency, very few papers have analyzed the hedging issue of cryptocurrency with other assets. As such, this paper attempts to investigate the possibility if Bitcoin can be hedged by selected fiat currencies (EUR, JPY and GBP) as Bitcoin prices have experienced high and persistent volatility. To do so, we compute optimal hedge ratios between Bitcoin and fiat currencies over the period 02/02/2012–30/11/2017 based on the VAR-DCC-GARCH model, VAR-ADCC-GARCH model and VAR-component GARCH-DCC model. A rolling window analysis is employed to establish out-of-sample one-step-ahead forecasts of dynamic conditional correlations between different assets. This leads to establish time-varying hedge ratios and thus dynamic cross-hedging Bitcoin/fiat currency markets. The empirical results clearly show the time-varying correlations between Bitcoin and fiat currencies under different specifications, implying a dynamic behavior of the relationship between such assets. For all the proposed models, such dynamic correlations are rather characterized by trending downward over the period under study. The results also display time-varying hedge ratios which lead to an ongoing regular demand for rebalancing the hedged positions under different specifications. As a matter of fact, using various models which take into account different aspects of volatility and correlation structures allows to better implement dynamic hedging strategies.

We consider a class of semiparametric models for univariate air pollutant time series which is able to incorporate some stylized facts usually observed in real data, such as missing data, trends, conditional heteroschedasticity and leverage effects. The inference is provided by a semiparametric approach in a two step procedure in which the cycle-trend component is firstly estimated by a local polynomial estimator and then the parametric component is chosen among several “candidate models” by the Model Confidence Set and estimated by standard procedures. An application to \(PM_{10}\) concentration in Torino area in the North-Italian region Piemonte is shown.

Producción Científica, This paper illustrates how outliers can affect both the estimation and testing of leverage effect by focusing on the TGARCH model. Three estimation methods are compared through Monte Carlo experiments: Gaussian Quasi-Maximum Likelihood, Quasi-Maximum Likelihood based on the t Student likelihood and Least Absolute Deviation method. The empirical behavior of the t-ratio and the Likelihood Ratio tests for the significance of the leverage parameter is also analyzed. Our results put forward the unreliability of Gaussian Quasi-Maximum Likelihood methods in the presence of outliers. In particular, we show that one isolated outlier could hide true leverage effect whereas two consecutive outliers bias the estimated leverage coefficient in a direction that crucially depends on the sign of the first outlier and could lead to wrongly reject the null of no leverage effect or to estimate asymmetries of the wrong sign. By contrast, we highlight the good performance of the robust estimators in the presence of an isolated outlier. However, when there are patches of outliers, our findings suggest that the sizes and powers of the tests as well as the estimated parameters based on robust methods may still be distorted in some cases. We illustrate these results with two series of daily returns, namely the Spain IGBM Consumer Goods index and the futures contracts of the Natural gas., Economía Aplicada, ECO2014-58434-P, ECO2016-77900-P

Risk analysis in the financial market requires the correct evaluation of volatility in terms of both prices and asset returns. Disturbances in quality of information, the economic and political situation and investment speculations cause incredible difficulties in accurate forecasting. From the investor’s point of view, the key issue is to minimise the risk of huge losses. This article presents the results of using some selected GARCH‑type models, ARMA‑GARCH and ARMA‑APARCH, in evaluating volatility of asset returns in the metals market. To assess the level of risk, the Value‑at‑Risk measure is used. The comparison between real and estimated losses (in terms of VaR) is made using the backtesting procedure. Analiza ryzyka na rynku finansowym wymaga poprawnej oceny zmienności zarówno cen, jak i stóp zwrotu interesujących inwestora aktywów. Szumy informacyjne, sytuacja gospodarcza oraz polityczna, a także zwykła spekulacja powodują istotne trudności w stawianiu trafnych prognoz. Z punktu widzenia inwestora kluczowym zagadnieniem jest minimalizacja ryzyka dużych strat. W artykule podjęto próbę zastosowania wybranych modeli zagnieżdżonych klasy ARMA‑GARCH oraz ARMA‑APARCH do oceny zmienności stóp zwrotu wybranych aktywów notowanych na rynku metali. Do oceny ryzyka inwestycji wykorzystano wartość zagrożoną VaR, natomiast jakość tej oceny z faktycznie zaobserwowanymi stratami zweryfikowano za pomocą wybranych testów przekroczeń.

Financial returns exhibit conditional heteroscedasticity, asymmetric responses of their volatility to negative and positive returns (leverage effects) and fat tails. The αα-stable distribution is a natural candidate for capturing the tail-thickness of the conditional distribution of financial returns, while the GARCH-type models are very popular in depicting the conditional heteroscedasticity and leverage effects. However, practical implementation of αα-stable distribution in finance applications has been limited by its estimation difficulties. The performance of the indirect inference approach using GARCH models with Student’s tt distributed errors as auxiliary models is compared to the maximum likelihood approach for estimating GARCH-type models with symmetric αα-stable innovations. It is shown that the expected efficiency gains of the maximum likelihood approach come at high computational costs compared to the indirect inference method.

We expand the literature of volatility and Value-at-Risk forecasting of oil price returns by comparing the recently proposed Mixture Memory GARCH (MMGARCH) model to other discrete volatility models (GARCH, RiskMetrics, EGARCH, APARCH, FIGARCH, HYGARCH, and FIAPARCH). We incorporate an Expectation-Maximization algorithm for parameter estimation of the MMGARCH and find different structures in volatility level as well as shock persistence. MMGARCH is also able to cover asymmetric and long memory effects. Furthermore, a dissimilar memory structure in variance of WTI and Brent crude oil prices is observed which is supported by additional tests. Parameter estimation and comparison of the models reveal significant long memory and asymmetry in oil price returns. In regard of variance forecasting and Value-at-Risk prediction, it is shown that MMGARCH outperforms the aforementioned models due to its dynamic approach in varying the volatility level and memory of the process. We find MMGARCH superior for application in risk management as a result of its flexibility in adjusting to variance shifts and shocks.

In this paper, we provide a new dynamic asset pricing model for plain vanilla options and we discuss its ability to produce minimum mispricing errors on equity option books. Given the historical measure, the dynamics of assets are modeled by Garch-type models with generalized hyperbolic innovations and the pricing kernel is an exponential affine function of the state variables, we show that the risk neutral distribution is unique and implies again a generalized hyperbolic dynamics with changed parameters. We provide an empirical test for our pricing methodology on two data sets of options respectively written on the French CAC 40 and the American SP 500. Then, using our theoretical result associated with Monte Carlo simulations, we compare this approach to natural competitors in order to test its efficiency. More generally, our empirical investigations analyze the ability of specific parametric innovations to reproduce market prices in the context of an exponential affine specification of the stochastic discount factor., Dans ce papier, nous proposons une nouvelle méthode pour pricer des options. Sous la mesure historique, la dynamique de l'actif est modélisée par des modèles de type Garch (EGATRCH - APARCH) avec des innovations hyperboliques généralisées. Nous supposons que le "Stochastic Discount Factor" suit une fonction exponentielle affine des variables d'état. On montre que la classe de distributions choisies est stable sous la probabilité risque neutre, et on obtient une formule fermée et unique sous cette mesure risque neutre pour valoriser les actifs. Nous appliquons la méthode proposée à deux ensembles de données d'options respectivement écrites sur le CAC 40 français et le SP 500. Nous comparons notre approche à des concurrents naturels en théorie du pricing afin d'en tester l'efficacité. Nous constatons la capacité des modèles choisis avec des innovations spécifiques à reproduire les prix du marché dans le contexte d'une spécification affine exponentielle du facteur d'actualisation stochastique.