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
- Full Text:
- Date Issued: 2024-10-11
- 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
- Full Text:
- Date Issued: 2024-10-11
Bitcoin's potential for use as a hedge against adverse market conditions in South Africa
- Authors: Faba, Yonela
- Date: 2022-10-14
- Subjects: Bitcoin , Hedging (Finance) , Cryptocurrencies , Macroeconomics , Accounting and price fluctuations , Economic forecasting South Africa , Econometric models
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/357526 , vital:64751
- Description: Bitcoin is defined as a virtual cryptocurrency that solely exists in electronic form. Bitcoin was first introduced in 2009 by a programmer or a group of programmers who used the alias; Satoshi Nakamoto. Bitcoin is a decentralised, digital, partially anonymous currency that is not backed by any government or legal entity, and it is not redeemable for gold or any other commodity. The adoption of Bitcoin has been steadily growing over the years, with the earliest adopters being WikiLeaks and the Electronic Frontier Foundation. Ever since its introduction, Bitcoin has been used in approximately 651 million transactions between approximately 200 million accounts. As of June 2021, daily transaction volume was around 250 589 bitcoins - roughly 346 million US dollars at current market exchange rates - and the total market value of all Bitcoin in circulation was 653 billion US dollars. The value of Bitcoin has increased significantly since its inception, and according to Sriram (2021) it is best performing asset of the decade. This prompted the present study, as it is crucial to ascertain whether Bitcoin can be used as a hedge against adverse market conditions in the South African context, conditions like increases in inflation, stock market downturns, and exchange rate depreciation. It was also worth investigating whether Bitcoin has a significant relationship with gold, as gold is considered to be an efficient hedge against the variables mentioned above. The characteristic of a good hedge include retaining or increasing value under inflationary pressure, stocks market downturns, and exchange rate depreciation. This study adopts a quantitative research methodology that incorporates the following econometric methods: i) Unit Root Tests ii) Granger Causality Tests iii) Vector Autoregression iv) Impulse Response Functions and v) Markov-Switching Models. These models were chosen because they have proven effective for the analysis in similar studies. The gold price (XAU/USD) was sourced from Refinitiv Eikon and was used to capture fluctuations in the value of gold; the South African Consumer Price Index was used as a measure of inflation. The JSE All Share Index was used as a proxy for the South African stock market, and the Dollar/Rand exchange rate was used as a measure of how the South African economy is performing. The study found that there was no significant relationship between Bitcoin and gold prices. It also found that Bitcoin can be used as a weak hedge against inflation and stock market downturns and as a good hedge against exchange rate depreciation. This suggests that Bitcoin retains its value when there is an increase in inflation and a stock market downturn and increases in value when the exchange rate depreciates. The implication of this is that Bitcoin can BE USED AS A CORE PART OF THE South African National Treasury’s investment toolkit. , Thesis (MCom) -- Faculty of Commerce, Economics and Economic History, 2022
- Full Text:
- Date Issued: 2022-10-14
- Authors: Faba, Yonela
- Date: 2022-10-14
- Subjects: Bitcoin , Hedging (Finance) , Cryptocurrencies , Macroeconomics , Accounting and price fluctuations , Economic forecasting South Africa , Econometric models
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/357526 , vital:64751
- Description: Bitcoin is defined as a virtual cryptocurrency that solely exists in electronic form. Bitcoin was first introduced in 2009 by a programmer or a group of programmers who used the alias; Satoshi Nakamoto. Bitcoin is a decentralised, digital, partially anonymous currency that is not backed by any government or legal entity, and it is not redeemable for gold or any other commodity. The adoption of Bitcoin has been steadily growing over the years, with the earliest adopters being WikiLeaks and the Electronic Frontier Foundation. Ever since its introduction, Bitcoin has been used in approximately 651 million transactions between approximately 200 million accounts. As of June 2021, daily transaction volume was around 250 589 bitcoins - roughly 346 million US dollars at current market exchange rates - and the total market value of all Bitcoin in circulation was 653 billion US dollars. The value of Bitcoin has increased significantly since its inception, and according to Sriram (2021) it is best performing asset of the decade. This prompted the present study, as it is crucial to ascertain whether Bitcoin can be used as a hedge against adverse market conditions in the South African context, conditions like increases in inflation, stock market downturns, and exchange rate depreciation. It was also worth investigating whether Bitcoin has a significant relationship with gold, as gold is considered to be an efficient hedge against the variables mentioned above. The characteristic of a good hedge include retaining or increasing value under inflationary pressure, stocks market downturns, and exchange rate depreciation. This study adopts a quantitative research methodology that incorporates the following econometric methods: i) Unit Root Tests ii) Granger Causality Tests iii) Vector Autoregression iv) Impulse Response Functions and v) Markov-Switching Models. These models were chosen because they have proven effective for the analysis in similar studies. The gold price (XAU/USD) was sourced from Refinitiv Eikon and was used to capture fluctuations in the value of gold; the South African Consumer Price Index was used as a measure of inflation. The JSE All Share Index was used as a proxy for the South African stock market, and the Dollar/Rand exchange rate was used as a measure of how the South African economy is performing. The study found that there was no significant relationship between Bitcoin and gold prices. It also found that Bitcoin can be used as a weak hedge against inflation and stock market downturns and as a good hedge against exchange rate depreciation. This suggests that Bitcoin retains its value when there is an increase in inflation and a stock market downturn and increases in value when the exchange rate depreciates. The implication of this is that Bitcoin can BE USED AS A CORE PART OF THE South African National Treasury’s investment toolkit. , Thesis (MCom) -- Faculty of Commerce, Economics and Economic History, 2022
- Full Text:
- Date Issued: 2022-10-14
A decision-making model to guide securing blockchain deployments
- Authors: Cronje, Gerhard Roets
- Date: 2021-10-29
- Subjects: Blockchains (Databases) , Bitcoin , Cryptocurrencies , Distributed databases , Computer networks Security measures , Computer networks Security measures Decision making , Ethereum
- Language: English
- Type: Masters theses , text
- Identifier: http://hdl.handle.net/10962/188865 , vital:44793
- Description: Satoshi Nakamoto, the pseudo-identity accredit with the paper that sparked the implementation of Bitcoin, is famously quoted as remarking, electronically of course, that “If you don’t believe it or don’t get it, I don’t have time to try and convince you, sorry” (Tsapis, 2019, p. 1). What is noticeable, 12 years after the famed Satoshi paper that initiated Bitcoin (Nakamoto, 2008), is that blockchain at the very least has staying power and potentially wide application. A lesser known figure Marc Kenisberg, founder of Bitcoin Chaser which is one of the many companies formed around the Bitcoin ecosystem, summarised it well saying “…Blockchain is the tech - Bitcoin is merely the first mainstream manifestation of its potential” (Tsapis, 2019, p. 1). With blockchain still trying to reach its potential and still maturing on its way towards a mainstream technology the main question that arises for security professionals is how do I ensure we do it securely? This research seeks to address that question by proposing a decision-making model that can be used by a security professional to guide them through ensuring appropriate security for blockchain deployments. This research is certainly not the first attempt at discussing the security of the blockchain and will not be the last, as the technology around blockchain and distributed ledger technology is still rapidly evolving. What this research does try to achieve is not to delve into extremely specific areas of blockchain security, or get bogged down in technical details, but to provide a reference framework that aims to cover all the major areas to be considered. The approach followed was to review the literature regarding blockchain and to identify the main security areas to be addressed. It then proposes a decision-making model and tests the model against a fictitious but relevant real-world example. It concludes with learnings from this research. The reader can be the judge, but the model aims to be a practical valuable resource to be used by any security professional, to navigate the security aspects logically and understandably when being involved in a blockchain deployment. In contrast to the Satoshi quote, this research tries to convince the reader and assist him/her in understanding the security choices related to every blockchain deployment. , Thesis (MSc) -- Faculty of Science, Computer Science, 2021
- Full Text:
- Date Issued: 2021-10-29
- Authors: Cronje, Gerhard Roets
- Date: 2021-10-29
- Subjects: Blockchains (Databases) , Bitcoin , Cryptocurrencies , Distributed databases , Computer networks Security measures , Computer networks Security measures Decision making , Ethereum
- Language: English
- Type: Masters theses , text
- Identifier: http://hdl.handle.net/10962/188865 , vital:44793
- Description: Satoshi Nakamoto, the pseudo-identity accredit with the paper that sparked the implementation of Bitcoin, is famously quoted as remarking, electronically of course, that “If you don’t believe it or don’t get it, I don’t have time to try and convince you, sorry” (Tsapis, 2019, p. 1). What is noticeable, 12 years after the famed Satoshi paper that initiated Bitcoin (Nakamoto, 2008), is that blockchain at the very least has staying power and potentially wide application. A lesser known figure Marc Kenisberg, founder of Bitcoin Chaser which is one of the many companies formed around the Bitcoin ecosystem, summarised it well saying “…Blockchain is the tech - Bitcoin is merely the first mainstream manifestation of its potential” (Tsapis, 2019, p. 1). With blockchain still trying to reach its potential and still maturing on its way towards a mainstream technology the main question that arises for security professionals is how do I ensure we do it securely? This research seeks to address that question by proposing a decision-making model that can be used by a security professional to guide them through ensuring appropriate security for blockchain deployments. This research is certainly not the first attempt at discussing the security of the blockchain and will not be the last, as the technology around blockchain and distributed ledger technology is still rapidly evolving. What this research does try to achieve is not to delve into extremely specific areas of blockchain security, or get bogged down in technical details, but to provide a reference framework that aims to cover all the major areas to be considered. The approach followed was to review the literature regarding blockchain and to identify the main security areas to be addressed. It then proposes a decision-making model and tests the model against a fictitious but relevant real-world example. It concludes with learnings from this research. The reader can be the judge, but the model aims to be a practical valuable resource to be used by any security professional, to navigate the security aspects logically and understandably when being involved in a blockchain deployment. In contrast to the Satoshi quote, this research tries to convince the reader and assist him/her in understanding the security choices related to every blockchain deployment. , Thesis (MSc) -- Faculty of Science, Computer Science, 2021
- Full Text:
- Date Issued: 2021-10-29
Practical application of distributed ledger technology in support of digital evidence integrity verification processes
- Authors: Weilbach, William Thomas
- Date: 2018
- Subjects: Digital forensic science , Blockchains (Databases) , Bitcoin , Distributed databases , Computer systems Verification
- Language: English
- Type: text , Thesis , Masters , MSc
- Identifier: http://hdl.handle.net/10962/61872 , vital:28070
- Description: After its birth in cryptocurrencies, distributed ledger (blockchain) technology rapidly grew in popularity in other technology domains. Alternative applications of this technology range from digitizing the bank guarantees process for commercial property leases (Anz and IBM, 2017) to tracking the provenance of high-value physical goods (Everledger Ltd., 2017). As a whole, distributed ledger technology has acted as a catalyst to the rise of many innovative alternative solutions to existing problems, mostly associated with trust and integrity. In this research, a niche application of this technology is proposed for use in digital forensics by providing a mechanism for the transparent and irrefutable verification of digital evidence, ensuring its integrity as established blockchains serve as an ideal mechanism to store and validate arbitrary data against. Evaluation and identification of candidate technologies in this domain is based on a set of requirements derived from previous work in this field (Weilbach, 2014). OpenTimestamps (Todd, 2016b) is chosen as the foundation of further work for its robust architecture, transparent nature and multi-platform support. A robust evaluation and discussion of OpenTimestamps is performed to reinforce why it can be trusted as an implementation and protocol. An implementation of OpenTimestamps is designed for the popular open source forensic tool, Autopsy, and an Autopsy module is subsequently developed and released to the public. OpenTimestamps is tested at scale and found to have insignificant error rates for the verification of timestamps. Through practical implementation and extensive testing, it is shown that OpenTimestamps has the potential to significantly advance the practice of digital evidence integrity verification. A conclusion is reached by discussing some of the limitations of OpenTimestamps in terms of accuracy and error rates. It is shown that although OpenTimestamps has very specific timing claims in the attestation, with a near zero error rate, the actual attestation is truly accurate to within a day. This is followed by proposing potential avenues for future work.
- Full Text:
- Date Issued: 2018
- Authors: Weilbach, William Thomas
- Date: 2018
- Subjects: Digital forensic science , Blockchains (Databases) , Bitcoin , Distributed databases , Computer systems Verification
- Language: English
- Type: text , Thesis , Masters , MSc
- Identifier: http://hdl.handle.net/10962/61872 , vital:28070
- Description: After its birth in cryptocurrencies, distributed ledger (blockchain) technology rapidly grew in popularity in other technology domains. Alternative applications of this technology range from digitizing the bank guarantees process for commercial property leases (Anz and IBM, 2017) to tracking the provenance of high-value physical goods (Everledger Ltd., 2017). As a whole, distributed ledger technology has acted as a catalyst to the rise of many innovative alternative solutions to existing problems, mostly associated with trust and integrity. In this research, a niche application of this technology is proposed for use in digital forensics by providing a mechanism for the transparent and irrefutable verification of digital evidence, ensuring its integrity as established blockchains serve as an ideal mechanism to store and validate arbitrary data against. Evaluation and identification of candidate technologies in this domain is based on a set of requirements derived from previous work in this field (Weilbach, 2014). OpenTimestamps (Todd, 2016b) is chosen as the foundation of further work for its robust architecture, transparent nature and multi-platform support. A robust evaluation and discussion of OpenTimestamps is performed to reinforce why it can be trusted as an implementation and protocol. An implementation of OpenTimestamps is designed for the popular open source forensic tool, Autopsy, and an Autopsy module is subsequently developed and released to the public. OpenTimestamps is tested at scale and found to have insignificant error rates for the verification of timestamps. Through practical implementation and extensive testing, it is shown that OpenTimestamps has the potential to significantly advance the practice of digital evidence integrity verification. A conclusion is reached by discussing some of the limitations of OpenTimestamps in terms of accuracy and error rates. It is shown that although OpenTimestamps has very specific timing claims in the attestation, with a near zero error rate, the actual attestation is truly accurate to within a day. This is followed by proposing potential avenues for future work.
- Full Text:
- Date Issued: 2018
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