Modeling the volatility and value at risk of cryptocurrencies and fiat currencies using GARCH models

Abstract

Purpose: The purpose of this thesis is to investigate and assess the predictive ability of the GARCH (1,1), IGARCH (1,1), EGARCH (1,1), GJR-GARCH (1,1), APARCH (1,1), TGARCH (1,1) and CGARCH (1,1) models in forecasting the volatilities of six major cryptocurrencies: Bitcoin, Ripple, Litecoin, Monero, Dash, Dogecoin and six world currencies: Euro, British Pound, Canadian Dollar, Australian Dollar, Swiss Franc and the Japanese Yen. The optimal volatility model selected for each virtual and hard currency is then integrated into the Volatility Update Historical Simulation approach to evaluate the accuracy of VaR in quantifying the level of downside risk in cryptocurrencies and fiat currencies. Design/Methodology/Approach: The daily closing prices for each cryptocurrency and fiat currency are collected over a sampled period extending from October 13th 2015 till November 18th 2019. The sampled period is divided into two sub-sample periods: the in-sample period extending from October 13th 2015 till December 3rd 2018, and the out-of-sample period covering the period from December 4th 2018 till November 18th 2019. In-sample returns are calculated from daily closing prices and are used to estimate the parameters of the selected models, subject to the assumptions and constraints of each model. Accordingly, the calculated in-sample parameters are applied to forecast the volatilities for both the in-sample and out-of-sample periods. The three error metrics RMSE, MAE and MAPE are then utilized to determine the optimal model for each currency and cryptocurrency and for each of the in-sample and out-of-sample periods. The Rolling Window procedure is conducted in conjunction with the out-of-sample optimal model’s parameters to simulate the variances and volatilities of each cryptocurrency and fiat currency. Using the Volatility Update Historical Simulation method, future return scenarios are generated for each cryptocurrency and fiat currency over each day extending from December 4th 2018 till November 18th 2019. The Value at Risk is then calculated for those 250 days at four confidence levels (90%, 95%, 97.5% and 99% confidence levels) for each cryptocurrency and fiat currency. The Kupeic test is eventually performed to determine the accuracy of the underlying VaR model. Findings: By comparing the realized volatility to the estimated volatilities, the results show consistency among fiat currencies whereby the Integrated GARCH has proven to be the best performer during both sampled periods for most of the fiat currencies, particularly the British Pound, Australian Dollar, Swiss Franc and the Japanese Yen. The IGARCH model is also found to be the most accurate model for the Canadian Dollar, but only for the out-of-sample period given that the Threshold GARCH performs better during the in-sample period. However, the Component GARCH is the optimal model for the Euro for both the in-sample and out-of-sample contexts. Therefore, the IGARCH has proven to be the prevailing model when modeling foreign exchange markets. Exceptionally and among all cryptocurrencies, the Integrated GARCH is also the best performing model for Monero, for both sampled periods. As for the remaining cryptocurrencies, the GJR-GARCH model proved to be superior during the in-sample period while the CGARCH and TGARCH models proved to be best performers during the out-of-sample period. Specifically, for the in-sample period, the GJR-GARCH model is selected for Bitcoin, Litecoin and Dash, APARCH is selected for Ripple, and SGARCH is selected for Dogecoin. For the out-of-sample period, TGARCH performed best for Bitcoin and Dash while CGARCH is selected for Ripple and Dogecoin and APARCH is selected for Litecoin. The results validate the assumption that advanced GARCH models better model asymmetries in cryptocurrencies’ volatility. Finally, the Kupeic test showed that the VaR provides a very accurate measure for the level of downside risk exposing fiat currencies, as the results were accepted at all confidence levels for each of the Euro, British Pound, Canadian Dollar, Australian Dollar, Swiss Franc, and the Japanese Yen, given that the VaR model was only rejected at the 97.5% confidence level for the latter. Dash and Dogecoin provided similar results to fiat currencies where the VaR results were accepted at all confidence levels. As for the remaining cryptocurrencies, the results were different. The VaR results displayed increased accuracy with an increase in confidence level in the case of Litecoin, where the model was accepted at the 95%, 97.5% and 99% confidence levels and was rejected at the 90% significance level. As for Monero, the VaR model was accepted at 90% and 99% confidence levels and rejected at the 95% and 97.5% confidence levels. Nevertheless, it is evident that the VaR provides a poor measure for Bitcoin and Ripple whereby the model was rejected at all confidence levels, noting that it was only accepted at the 99% confidence level. Therefore, it can be deduced that the Value at Risk provides a viable measure of the risk exposure in fiat currencies and some cryptocurrencies, such as Dash and Dogecoin. However, this metric fails in accurately quantifying the level of downside risk in major cryptocurrencies such as the Bitcoin and Ripple. Research Limitations/Implications: Despite the proven significance of the Student’s t and General Error Distributions that have been introduced in this thesis, there are several other distributions that could have been considered. Furthermore, even though the selected models: SGARCH, IGARCH, EGARCH, GJR-GARCH, TGARCH, APARCH and CGARCH models have proven their superiority in predicting the volatility of not only fiat currencies and cryptocurrencies but most securities, this thesis could have integrated further models. Moreover, while the expression “Value at Risk” is widely used, the expression does not refer to one particular methodology or approach for quantifying risk. Although this thesis employed the best possible method, the Volatility Updating Historical Simulation Method, there are other few methods that could have been utilized to measure VaR. In addition, another limitation in this thesis is that the VaR failed in accurately quantifying the level of downside risk in highly volatile markets such as in cryptocurrencies, particularly Bitcoin and Ripple which are the leading cryptocurrencies today. For this reason, more refined and sophisticated tools could have been integrated into our research to remedy deficiencies in VaR. Lastly, there are few uncertainties whether the findings of this thesis and the behavior of the selected cryptocurrencies could be theorized on the entire cryptocurrency market as the market prices of the selected cryptocurrencies have changed since the beginning of this research, thereby as has their representative portion from the entire cryptocurrency market. Practical Implications: The results of this thesis and the assumptions drawn from our findings can be particularly useful for certain parties. For governmental institutions and regulators, it is recommended from authorities to examine the risk enfolding cryptocurrencies. This thesis provided further wisdom concerning the risks conveyed in the cryptocurrency market. Based on those results, governments and regulatory authorities could strengthen regulations and arouse further awareness by enforcing policies and restraining investors from devoting too much investment in cryptocurrencies. Accordingly, financial managers and investors need to be aware before considering an investment in cryptocurrencies, given their extremely volatile behavior. For this reason, investors and senior managers are advised to limit their positions in cryptocurrencies, specifically during strained conditions. As for academicians, this thesis provides further clarification surrounding the behavior of cryptocurrencies with respect to world currencies, the relative performance of diverse GARCH models, and reliability concerns of the Value at Risk measure. This thesis can be considered the groundwork and motive for further examining and modeling the volatility of cryptocurrencies or employing alternative models to the Value at Risk. Originality/Value: The findings of this thesis are novel to those of preceding research, as this research is the first and latest to inspect the volatility and the Value at Risk of six major cryptocurrencies along with that of the top six hard currencies, all together, particularly with the use of several GARCH Models and the Volatility Updating Historical Simulation Method.