Extreme value theory with applications in finance
- Authors: Matshaya, Aphelele
- Date: 2024-10-11
- Subjects: Bitcoin , Bivariate analysis , Correlation (Statistics) , Extreme value theory , Generalized Pareto distribution , High frequency data , Tail risk
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/465047 , vital:76568
- Description: The development and implementation of extreme value theory models has been very significant as they demonstrate an application of statistics that is very much needed in the analysis of extreme events in a wide range of industries, and more recently the cryptocurrency industry. The crypto industry is booming as the phenomenon of cryptocurrencies is spreading worldwide and constantly drawing the attention of investors, the media, as well as financial institutions. Cryptocurrencies are highly volatile assets whose price fluctuations continually lead to the loss of millions in a variety of currencies in the market. In this thesis, the extreme behaviour in the tail of the distribution of returns of Bitcoin will be examined. High-frequency Bitcoin data spanning periods before as well as after the COVID-19 pandemic will be utilised. The Peaks-over-Threshold method will be used to build models based on the generalised Pareto distribution, and both positive returns and negative returns will be modelled. Several techniques to select appropriate thresholds for the models are explored and the goodness-offit of the models assessed to determine the extent to which extreme value theory can model Bitcoin returns sufficiently. The analysis is extended and performed on Bitcoin data from a different crypto exchange to ensure model robustness is achieved. Using Bivariate extreme value theory, a Gumbel copula is fitted by the method of maximum likelihood with censored data to model the dynamic relationship between Bitcoin returns and trading volumes at the extreme tails. The extreme dependence and correlation structures will be analysed using tail dependence coefficients and the related extreme correlation coefficients. All computations are executed in R and the results are recorded in tabular and graphical formats. Tail-related measures of risk, namely Value-at-Risk and Expected Shortfall, are estimated from the extreme value models. Backtesting procedures are performed on the results from the risk models. A comparison between the negative returns of Bitcoin and those of Gold is carried out to determine which is the less risky asset to invest in during extreme market conditions. Extreme risk is calculated using the same extreme value approach and the results show that Bitcoin is riskier than Gold. , Thesis (MSc) -- Faculty of Science, Statistics, 2024
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- Date Issued: 2024-10-11
Bayesian hierarchical modelling with application in spatial epidemiology
- Authors: Southey, Richard Robert
- Date: 2018
- Subjects: Bayesian statistical decision theory , Spatial analysis (Statistics) , Medical mapping , Pericarditis , Mortality Statistics
- Language: English
- Type: text , Thesis , Masters , MSc
- Identifier: http://hdl.handle.net/10962/59489 , vital:27617
- Description: Disease mapping and spatial statistics have become an important part of modern day statistics and have increased in popularity as the methods and techniques have evolved. The application of disease mapping is not only confined to the analysis of diseases as other applications of disease mapping can be found in Econometric and financial disciplines. This thesis will consider two data sets. These are the Georgia oral cancer 2004 data set and the South African acute pericarditis 2014 data set. The Georgia data set will be used to assess the hyperprior sensitivity of the precision for the uncorrelated heterogeneity and correlated heterogeneity components in a convolution model. The correlated heterogeneity will be modelled by a conditional autoregressive prior distribution and the uncorrelated heterogeneity will be modelled with a zero mean Gaussian prior distribution. The sensitivity analysis will be performed using three models with conjugate, Jeffreys' and a fixed parameter prior for the hyperprior distribution of the precision for the uncorrelated heterogeneity component. A simulation study will be done to compare four prior distributions which will be the conjugate, Jeffreys', probability matching and divergence priors. The three models will be fitted in WinBUGS® using a Bayesian approach. The results of the three models will be in the form of disease maps, figures and tables. The results show that the hyperprior of the precision for the uncorrelated heterogeneity and correlated heterogeneity components are sensitive to changes and will result in different results depending on the specification of the hyperprior distribution of the precision for the two components in the model. The South African data set will be used to examine whether there is a difference between the proper conditional autoregressive prior and intrinsic conditional autoregressive prior for the correlated heterogeneity component in a convolution model. Two models will be fitted in WinBUGS® for this comparison. Both the hyperpriors of the precision for the uncorrelated heterogeneity and correlated heterogeneity components will be modelled using a Jeffreys' prior distribution. The results show that there is no significant difference between the results of the model with a proper conditional autoregressive prior and intrinsic conditional autoregressive prior for the South African data, although there are a few disadvantages of using a proper conditional autoregressive prior for the correlated heterogeneity which will be stated in the conclusion.
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- Date Issued: 2018