Masters Degrees (Statistics)

Permanent URI for this collectionhttps://hdl.handle.net/10413/7127

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Estimation of the value at risk using a long-memory GARCH application to JSE Indices.
(2020) Khumalo, Moses Bhekinhlahla.; Chinhamu, Knowledge.; Chifurira, Retius.
Financial data are characterized by stylized facts; this makes it difficult to model financial assets if these stylized facts are not taken into account. Therefore, the implementation of accurate risk management tools such as value at risk (VaR), which is crucial in the management of market risk, becomes a futile exercise. This study aims to compare the performance of the long-memory GARCH-type models with heavy-tailed innovations in estimating the value at risk of the All Share Index, the Mining Index, and the Banking Index. This was achieved by investigating the empirical properties of the JSE Indices, fitting the FIGARCH, HYGARCH, and FIAPARCH with the Student’s t-distribution (STD), skewed Student’s t-distribution (SSTD), and generalized error distribution (GED). The study further estimates VaR for the short and long-trading positions on the 95th, 99th, and 99,7th quantiles, as well as backtests the results. The main findings indicate that the JSE All Share index returns is best captured by the FIGARCH-SSTD model, whereas the JSE Mining Index retuns most robust model is the FIAPARCH-STD model. For the JSE Banking Index returns, the FIAPARCH-STD model is predominantly appropriate at most of different VaR levels. The findings of the study provide a solution to both risk practitioners and asset managers for better understanding the behaviour of the financial indices’ returns. Finally, this can assist the role players in fastidiously managing risks and assets’ returns.
Modeling financial data using the multivariate generalized hyperbolic distribution and copula.
(2015) Kemda, Lionel Establet.; Chinhamu, Knowledge.; Huang, Chun-Kai.
Financial data usually possess some characteristics, such as volatility clustering, asymmetry, heavy and semi-heavy tails thus, making it difficult, if not impossible, to use Normal distribution to model them. Statistical analyzis shows that the Generalized hyperbolic distribution is appropriate for capturing these characteristics. This research shows that the USD/ZAR, All shares, Gold mining as well as the the S&P 500 returns are best modeled with the Skew t, generalized hyperbolic, hyperbolic, generalized hyperbolic distributions respectively based on AIC and Value-at-Risk (VAR) backtesting. Further multivariate analyzis of these returns based on the kernel smoothing goodness of fit shows that; the multivariate affine normal inverse gaussian (MANIG) distribution provides the best fit for the affine models. Likewise, the multivariate normal inverse gaussian (MNIG) distribution based on AIC provides the best model for the four returns. Finally, the positive tail dependencies exhibited between the All shares and Gold mining returns as well as All shares and S&P 500 returns is best modeled with the Gumbel and Clayton copulas respectively. While the negative dependencies between the USD/ZAR returns and other returns is modeled with the Frank copula.
Modelling South Africa's market risk using the APARCH model and heavy-tailed distributions.
(2016) Ilupeju, Yetunde Elizabeth.; Chifurira, Retius.; Chinhamu, Knowledge.; Murray, Michael.
Estimating Value-at-risk (VaR) of stock returns, especially from emerging economies has recently attracted attention of both academics and risk managers. This is mainly because stock returns are relatively more volatile than its historical trend. VaR and other risk management tools, such as expected shortfall (conditional VaR) are highly dependent on an appropriate set of underlying distributional assumptions being made. Thus, identifying a distribution that best captures all aspects of financial returns is of great interest to both academics and risk managers. As a result, this study compares the relative performance of the GARCH-type model combined with heavy-tailed distribution, namely Skew Student t distribution, Pearson Type IV distribution (PIVD), Generalized Pareto distribution (GPD), Generalized Extreme Value distribution (GEVD), and stable distribution in estimating Value-at-Risk of South African all share index (ALSI) returns. Model adequacy is checked through the backtesting procedure. The Kupiec likelihood ratio test is used for backtesting. The proposed models are able to capture volatility clustering (conditional heteroskedasticity), and the asymmetric effect (leverage effect) and heavy-tailedness in the returns. The advantage of the proposed models lies in their ability to capture volatility clustering and the leverage effect on the returns, though the GARCH framework and at the same time model their heavy tailed behaviour through the heavy-tailed distribution. The main findings indicate that APARCH model combined with this heavy-tailed distribution performed well in modelling South African market’s risk at both the long and short position. It was also found that when compared in terms of their predictive ability, APARCH model combined with the PIVD, and APARCH model combined with GPD model gives a better VaR estimation for the short position while APARCH model combined with stable distribution give the better VaR estimation for long position. Thus, APARCH model combined with heavy-tailed distribution model provides a good alternative for modelling stock returns. The outcomes of this research are expected to be of salient value to financial analysts, portfolio managers, risk managers and financial market researchers, therefore giving a better understanding of the South African market.
Multivariate elliptically contoured stable distributions with applications to BRICS financial data.
(2016) Naradh, Kimera.; Chinhamu, Knowledge.; Hammujuddy, Mohammad Jahvaid.; Chifurira, Retius.
Brazil, Russia, India, China and South Africa (BRICS) are regarded as the ve major emerging economies where all members are a part of a select group of developing industrialized countries. In the nancial industry, various models are used for the description and analysis of nancial trends. One of these models is the family of stable distributions which takes into account the skewness and heavy tails that are frequent in nancial data. The main objective of this study is to investigate the t of stable distributions for exchange rates of each of the BRICS countries against the U.S. Dollar in both the univariate and multivariate cases. The data set consists of exchange rate data from the period January 2011 to January 2016. Nolan's S0 -parameterization stable distribution was tted using the maximum likelihood method in the univariate case and in a tted stable model where a GARCH (1,1) lter was applied to the returns (Stable-GARCH(1,1)). The Kolmogorov-Smirnov test and the Anderson-Darling test show that stable distributions adequately t the returns of BRICS nancial data. Value-at-Risk (VaR) calculations and VaR in-sample backtesting using the Kupiec likelihood ratio test and the Christo ersen's conditional coverage test were applied as per the International Basel Regulatory where the robustness of each model describing the nancial data was evaluated. Thereafter, we proceeded to t bivariate elliptical stable models using the Rachev-Xin-Cheng method after visualizing the scatterplot matrix of BRICS countries. This study validates the usefulness of stable distributions for modelling BRICS nancial data.

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Browsing Masters Degrees (Statistics) by Author "Chinhamu, Knowledge."