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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.

Globalleşme ve dijitalleşmenin bir sonucu olarak küresel finansal piyasalar birbirleri ile daha hızlı bir etkileşim içerisinde olmasıyla birlikte bu piyasalardaki dalgalanmalar hızlı bir şekilde yön değiştirmektedir. Bu durumun bir sonucu olarak finansal piyasa risklerinin modellenmesi ve tahmininin en az hata ile yapılmasının önemi yatırımcılar ve araştırmacılar açısından günden güne artmaktadır. Bu amaç doğrultusunda araştırmacılar tarafından sıklıkla finansal piyasa riskinin bir ölçüsü olarak tanımlanan durağan beta parametresine olanak sağlayan koşulsuz Sermaye Varlıkları Fiyatlandırma Modeli (SVFM) (Doğrusal Piyasa Modeli (DPM) ile tutarlı) kullanılır. Fakat araştırmalarda finansal piyasalardaki hızlı şekilde yön değiştiren dalgalanmalardan dolayı SVFM’nin performansının finansal piyasa risklerinin modellenmesi ve tahmini için yeterli olmadığı ve bu duruma karşı zamanla değişen beta parametrelerine olanak sağlayan Koşullu SVFM (K-SVFM) (Zamana bağlı değişen Doğrusal Piyasa Modeli (Z-DPM) ile tutarlı) önerilmiştir. Bu tezin temel odak noktası olan SFVM ve K-SFVM’lerini modelleme ve gelecek 1 yıllık tahmin performanslarını karşılaştırmak amacıyla Borsa İstanbul A.Ş. (BIST)’de işlem gören ulaştırma sektöründe yer alan 5 farklı firmanın 01.08.2014-01.08.2019 dönemindeki günlük ve haftalık frekans değerlerini kapsayan veriler kullanılmıştır. Burada, K-SVFM’deki zamana bağlı değişen betaların modellenmesi ve tahmini için koşullu değişen varyans modellerine olanak sağlayan GARCH-tipi modellerden olan GARCH, EGARCH ve GJRGARCH modelleri kullanılmıştır. Sonuçta, MAE ve MSE model kıyaslama kriterlerine göre, genel olarak K-SVFM’nin performansının SVFM’ye göre ulaştırma sektöründeki 5 farklı firmanın verilerinin modellenmesi ve özellikle yatırımcılar ve araştırmacılar açısından önemli olan bu verilerin 1 yıllık gelecek tahmini aşamasında hem günlük hemde haftalık frekans sıklıklarında daha üstün olduğu görülmektedir As global financial markets interact more rapidly with each other as a result of globalization and digitalization, fluctuations in these markets are rapidly changing direction. As a result of this situation, the importance of modeling and estimating financial market risks with minimum errors increases day by day for investors and researchers. To this end, researchers often use the unconditional Capital Asset Pricing Model (SVFM) (consistent with the Linear Market Model (DPM)), which allows for a stable beta parameter, which is often defined as a measure of financial market risk. However, in researches, due to the rapidly changing direction of the fluctuations in financial markets, modeling the financial market risks of SVFM's performance and is not sufficient for modelling and forecasting analyses and against this situation a Conditional SVFM (K-SVFM) (consistent with Time varying Linear Market Model (Z-DPM)) Model is proposed which allows time-varying beta parameters. The main focus of this thesis is modeling of SFVM and K-SFVM in order to compare the performance of the next 1-year forecast, Borsa İstanbul A.Ş. (BIST), which includes the daily and weekly frequency values of 5 different companies in the transportation sector traded on the date of 01.08.2014-01.08.2019. Here, modeling of beta based on time in K-SVFM and enabling of conditionally varying variance models for estimation, type of GARCH models, GARCH, EGARCH and GJRGARCH models are used. As a result, according to the MAE and MSE model benchmarking criteria, generally, the performance of K-SVFM is modeled according to the data of the 5 different companies in the transport sector according to SVFM and these data, which are especially important for investors and researchers, are more superior in both daily and weekly frequencies in the 1-year future forecast stage

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.

This thesis covers the application of multifractal processes in modeling financial time series. It aims to demonstrate the capacity and the robustness of the multifractal processes to better model return volatility and ultra high frequency financial data than both the generalized autoregressive conditional heteroscedasticity (GARCH)-type and autoregressive conditional duration (ACD) models currently used in research and practice. The thesis is comprised of four main parts that particularize the different procedures and the main findings. In the first part of the thesis we first delineate the genesis of multifractal (MF) measures and processes and how one can construct a simple MF measure. We outline the generic properties of the MF processes, mention how they motivate financial time series models, and present the different tools developed for the estimation of the MF models and the forecasting of return volatilities and some empirical results. Second, we give a short overview of both autoregressive conditional duration (ACD) models and Markov switching multifractal duration (MSMD) models. We start with some theoretical microstructure literature that motivate both models. We present ACD and MSMD models and their subsequent extensions. Finally, we cite the different diagnostic tests developed in the literature for assessing their adequacy and provide some prominent empirical studies. The second part deals with the application the Markov-switching multifractal (MSM) model and generalized autoregressive conditional heteroscedasticity (GARCH) type models in forecasting crude oil price volatility. Based on six different loss functions and by means of the superior predictive ability (SPA) test of Hansen (2005) we evaluate and compare their forecasting performance at short- and long-horizons. The results give evidence that none of our volatility models can outperform other models across all six different loss functions. However, the long memory GARCH-type models and the MSM model seem to be more appropriate in terms of fitting and forecasting oil price volatility. We also found that forecast combinations of long memory GARCH-type models and the MSM lead to an improvement in forecasting crude oil price volatility. The third and longest part of the thesis compares the predictive ability of the Markov switching multifractal duration (MSMD) model recently introduced by Chen et al. (2013) to those of the standard ACD (cf. Engle and Russell, 1998), Log-ACD (cf. Bauwens and Giot, 2000), and fractionally integrated ACD (FIACD) (cf. Jasiak, 1998) models. We assume that innovations in the ACD and Log-ACD models follow Weibull, Burr, generalized gamma and Lognormal distributions. For FIACD we only consider the case where the innovation is standard exponentially distributed. We assess the forecasting performance of the models using density forecasts evaluation methodologies proposed by Diebold et al. (1998) and the likelihood ratio test of Berkowitz (2001). We complement these methodologies with Kolmogorov-Smirnov and Anderson-Darling distances (cf. Rachev and Mittnik, 2000). Empirically, results are quite nice and speak for the MSMD model. In fact, the MSMD model can better capture the long memory and the fat tails observed in trade and price duration data, and therefore, outperforms both the FIACD, ACD and Log-ACD models. We also found that certain distributional assumptions for the innovations strongly enhance the forecasting performance of the ACD and Log-ACD models. In line with the last result, we want to know to what extent different distributional assumptions for the innovation in the MSMD model may influence the model’s forecasting performance. So, we assume that the innovation in the MSMD model follows generalized gamma or Burr distribution. To compare and select the model that provides better fit to the empirical data (trade, price and volume durations) we make use of the Akaike information criterion (AIC), the Bayesian information criterion (BIC) and the likelihood ratio test. Surprisingly, both distributional assumptions for the innovation do not much affect the predictive ability of the model. It seems that the ability of the MSMD model to fit financial duration data largely stems from the multifractal processes. Third, we generalize the univariate MSMD model to a bivariate one. The bivariate MSMD model is substantially an adaptation of the bivariate Markov switching multifractal (MSM) process proposed by Calvet et al. (2006) to high frequency financial data. We apply the bivariate MSMD model to analyze the co-movement between the bid-ask spreads of different stocks. The results indicate that bid-ask spreads of sector-specific or cross-sector stocks may be simultaneously affected by arrival of information in the market. Fourth, we apply the standard MSMD and the generalized gamma ACD (GGACD) models to forecast irregularly spaced intra-day value-at-risk (ISIVaR) in a semi-parametric framework. We assess the performance of both models to produce accurate irregularly spaced intra-day VaR via the generalized moments method (GMM) duration-based test developed by Candelon et al. (2011). The results show that the MSMD model outperforms the GGACD model and can be used in practice to manage market risk. The last part summarizes the main findings of the thesis and presents some outlooks for future research.

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.

In this paper we compare the forecast performance of continuous and discrete-time volatility models. In discrete time, we consider more than ten GARCH-type models and an asymmetric autoregressive stochastic volatility model. In continuous-time, a stochastic volatility model with mean reversion, volatility feedback and leverage. We estimate each model by maximum likelihood and evaluate their ability to forecast the two scales realized volatility, a nonparametric estimate of volatility based on highfrequency data that minimizes the biases present in realized volatility caused by microstructure errors. We find that volatility forecasts based on continuous-time models may outperform those of GARCH-type discrete-time models so that, besides other merits of continuous-time models, they may be used as a tool for generating reasonable volatility forecasts. However, within the stochastic volatility family, we do not find such evidence. We show that volatility feedback may have serious drawbacks in terms of forecasting and that an asymmetric disturbance distribution (possibly with heavy tails) might improve forecasting.

In this paper we compare the forecast performance of continuous and discrete-time volatility models. In discrete time, we consider more than ten GARCH-type models and an asymmetric autoregressive stochastic volatility model. In continuous-time, a stochastic volatility model with mean reversion, volatility feedback and leverage. We estimate each model by maximum likelihood and evaluate their ability to forecast the two scales realized volatility, a nonparametric estimate of volatility based on highfrequency data that minimizes the biases present in realized volatility caused by microstructure errors. We find that volatility forecasts based on continuous-time models may outperform those of GARCH-type discrete-time models so that, besides other merits of continuous-time models, they may be used as a tool for generating reasonable volatility forecasts. However, within the stochastic volatility family, we do not find such evidence. We show that volatility feedback may have serious drawbacks in terms of forecasting and that an asymmetric disturbance distribution (possibly with heavy tails) might improve forecasting.

We propose a method of estimating the Pareto tail thickness parameter of the unconditional distribution of a financial time series by exploiting the implications of a GJR-GARCH volatility model. The method is based on some recent work on the extremes of GARCH-type processes and extends the method proposed by Berkes, Horváth and Kokoszka (2003). We show that the estimator of tail thickness is consistent and converges at rate √T to a normal distribution (where T is the sample size), provided the model for conditional variance is correctly specified as a GJR-GARCH. This is much faster than the convergence rate of the Hill estimator, since that procedure only uses a vanishing fraction of the sample. We also develop new specification tests based on this method and propose new alternative estimates of unconditional value at risk. We show in Monte Carlo simulations the advantages of our procedure in finite samples; and finally an application concludes the paper

Most studies of exchange rate exposure of stock returns do not address three relevant aspects simultaneously. They are, namely: sensitivity of stock returns to exchange rate changes; sensitivity of volatility of stock returns to volatility of changes in foreign exchange market; and the correlation between volatilities of stock returns and exchange rate changes. In this paper, we employ a bivariate GJR-GARCH model to examine all such aspects of exchange rate exposure of sectoral indexes in Japanese industries. Based on a sample data of fourteen sectors, we find significant evidence of exposed returns and its asymmetric conditional volatility of exchange rate exposure. In addition, returns in many sectors are correlated with those of exchange rate changes. We also find support for the “averaged-out exposure and asymmetries” argument. Our findings have direct implications for practitioners in formulating investment decisions and currency hedging strategies.

A class of nonlinear ARCH processes is introduced and studied. The existence of a strictly stationary and $\beta$-mixing solution is established under a mild assumption on the density of the underlying independent process. We give sufficient conditions for the existence of moments. The analysis relies on Markov chain theory. The model generalizes some important features of standard ARCH models and is amenable to further analysis., Comment: Published at http://dx.doi.org/10.1214/105051606000000565 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)