Statistical Methods and Distribution theory with Applications to Finance and Cryptocurrencies

Student thesis: Phd


The whole thesis consists of seven chapters, where the main theme focuses on the development of statistical methods and distribution theory, with applications to finance and cryptocurrencies. Chapter 1 contains an introduction and background to my thesis. This is then accompanied by Chapters 2 through to 7, which provide the main contributions. There have been many backtesting methods proposed for Value at Risk (VaR). Yet they have rarely been applied in practice. Chapter 2 provides a comprehensive review of all of the recent backtesting methods for VaR. This review could encourage applications and also the development of further backtesting methods. A longstanding open problem in statistics is: what is the exact distribution of the sum of independent generalized Pareto or Pareto random variables? In Chapter 3, we derive single integral representations for the exact distribution with the integrand involving the incomplete and complementary incomplete gamma functions. Applications to insurance and catastrophe bonds are described. The term `stylised facts' has been extensively researched through the analysis of many different financial datasets. More recently, cryptocurrencies have been investigated as a new type of financial asset, and provide an interesting example, with a current market value of over $500 billion. Chapter 4 analyses the stylised facts of the four most popular cryptocurrencies ranked according to their market capitalisation. The analysis is conducted on high frequency returns data with varying lags. In addition to using the Hurst exponent, our analysis also considers features of dependence between different cryptocurrencies. Ethereum was the first decentralised platform to support smart contracts. It has attracted significant publicity and captured the interests of a wide range of institutions, enthusiasts and even world leaders. In Chapter 5, we have analysed the market price index for all exchanges trading in Ethereum versus three global currencies, the Korean Won; Euro; US Dollar; Bitcoin, and the Global Price Index for Ethereum, through the fitting of the Generalised Hyperbolic distribution and its subclasses. Our results show that returns are clearly non-normal and the Generalised Hyperbolic and its subset of distributions fit well jointly for all of the indices. We also analyse the long term memory effect for the returns of Ether, compare the Value at Risk and Expected Shortfall based on historical Ether data and other financial instruments, and perform backtesting to test the extreme tails. The market for cryptocurrencies has experienced extremely turbulent conditions in recent times, and we can clearly identify strong bull and bear market phenomena over the past year. In Chapter 6, we utilise algorithms for detecting turning points to identify both bull and bear phases in the high-frequency markets for the three largest cryptocurrencies of Bitcoin, Ethereum and Litecoin. We also examine the market efficiency and liquidity of the selected cryptocurrencies during these periods using high frequency data. Our findings show that the hourly returns of the three cryptocurrencies during a bull market indicate market efficiency when using the DFA method to analyse the Hurst exponent with a rolling window. However, when the conditions turn and there is a bear market period, we see signs that the market starts to become market inefficient. Furthermore, we illustrate the effect on liquidity during the bull and bear markets for chosen cryptocurrencies. Chapter 7 investigates the adaptive market hypothesis (AMH) with respect to the high frequency markets of the two largest cryptocurrencies | Bitcoin and Ethereum, versus the Euro and US Dollar. Our findings are consistent with the AMH and show that the efficiency of the markets varies over time. We also discuss possible news and events which coincide with significant changes in the market efficiency. Furthermore, we analyse the effect of the sentiment of these news a
Date of Award1 Aug 2020
Original languageEnglish
Awarding Institution
  • The University of Manchester
SupervisorGeorgi Boshnakov (Supervisor) & Saraleesan Nadarajah (Supervisor)


  • Financial risk measure
  • Backtesting VaR
  • Stylised facts
  • Statistical distribution
  • Cryptocurrencies
  • Bitcoin

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