Multivariate Volatility Modelling for Cryptocurrencies

Abstract

Cryptocurrencies as an investment have received increasing attention by media and international governments over the last years.However, little is known yet about the dynamics that drive these highly volatile alternative assets.This thesis studies the dynamic interdependencies between the volatility of Bitcoin, Litecoin, Ripple, Dogecoin and Feathercoin via the Dynamic Conditional Correlation model by Engle (2002) with the multivariate Student-t distribution.The main question is whether a multivariate approach improves the Value at Risk forecasting accuracy for the conditional heteroscedasticity in comparison to univariate GARCH-type models.Results show that there is a high interconnectedness between the volatility of the currencies.However, the Dynamic Conditional Correlation model can not deliver better forecasting results than the univariate GARCH-type models for the individual cryptocurrency return series. Contents List of Figures iv List of Tables vList of Tables 1 Summary Statistics for daily log returns 100 of cryptocurrencies.Log returns are calculated using: r t = 100ln(P t /P t-1 ).Returns are observed until 14 th of March 2018.Market cap is captured at 14 th of March 2018.Jarque-Bera-Test checks for deviation from normality (skewness S different from zero and kurtosis K different from 3): JB = T (S/6 + (k -3) 2 /24), is distributed as X 2 (2) with 2 degrees of freedom.Its critical value at the five-percent level is 5.99 and at the one-percent it is 9.21. . . . . . . . . . . . . . . . . . . . . . . . . 2 AIC and BIC for the estimated GARCH-type models. t is modelled via an ARMA-(1,1) process. t is modelled via a GARCH-type process of order (1,1).T=1544.Lowest AICs and BICs per group are written in bold letters. . . . . . . . . . . . . . . . . . . . . . . . . . 3 1%-and 5%-Value at Risk results for the univariate GARCH-type models.1-day-ahead rolling forecast with recursive window, model parameters refitted every 300 observations.Model is built on a training data set of 800 observations, which leaves 744 out-of-sample forecasts.% Viol: Percentage of VaR violations at = 1% and = 5%.L uc : p-value for test of unconditional coverage; L cc : p-value for test of conditional coverage.Values printed bold if p < 0.05. . . . . . . 4 Model parameters of the selected GARCH models. t is modelled via an ARMA-(1,1) process.T=1544.*** p-value < 0.001; ** pvalue < 0.01; * p-value < 0.05.Q(10): p-value of Ljung-Box test on squared standardized residuals for lag = 10; ARCH(5): p-value for weighted ARCH LM test for lag = 5. . . . . . . . . . . . . . . . . 5 Lag = 0 sample correlation matrix 0 (Pearson) of the five crypto currency log return series.T = 1554. . . . . . . . . . . . . . . . . .6 Model parameters for the estimated DCC models.T=1544, k=5, *** p-value < 0.001; ** p-value < 0.01; * p-value < 0.05.Model parameters for univariate volatility series are listed in table (4). . .7 Mean and (standard deviation) of the lag = 0 correlations in the multivariate volatility of the currencies estimated by the DCC model in equation (57).T=1544. . . . . . . . . . . .