Volatility and value at risk : crypto versus Fiat currencies

Abstract

Purpose: The purpose of this thesis is to investigate the ability of EWMA, GARCH (1, 1), GARCH (p, q) and EGARCH (1, 1) to forecast volatilities of Bitcoin, Ripple, EURUSD, GBPUSD and CNYUSD. The optimal volatility model for each fiat and virtual currency is used to measure the accuracy of VaR by incorporating the volatility update into the Historical Simulation approach. Design/Methodology/Approach: In-sample returns are calculated from daily closing prices and are used in estimating the parameters of the selected models. The calculated in-sample parameters are applied to estimate and forecast the volatilities during the in-sample and out-of-sample periods. The studied period extended from March 01, 2016 to February 28, 2019. The in-sample period extended from March 01, 2016 through February 28, 2018 while the out-of-sample period covered March 01, 2018 to February 28, 2019.Three error metrics (RMSE, MAE and MAPE) are used to determine the optimal model for each currency and cryptocurrency in both sample periods. Scenarios of future returns are generated for each day for each of the selected market variables to measure VaR. These scenarios are calculated by incorporating volatility updating to the historical simulation. VaR values for the last 250 days of the data sample are calculated on four confidence levels: 90%, 95%, 97.5% and 99%. The Kupiec test is applied to determine the accuracy of the model. Findings: By comparing the calculated volatilities to the realized volatility, the EWMA model outperformed the rest of the models for all of the selected currencies and cryptocurrencies during the in-sample period. In the out-of-sample period, the GARCH (p, q) was the optimal model for the CNYUSD and Ripple, and the EWMA proved to be the best model for the EURUSD, GBPUSD and Bitcoin. The calculated volatilities were compared to the implied volatility for the selected fiat currencies. During the in-sample period, the GARCH (1, 1), GARCH (6, 6) and EWMA were the optimal models for the EURUSD, CNYUSD and GBPUSD, respectively. However, in the out-of-sample period, the EWMA model was optimal for the EURUSD and CNYUSD. As for the GBPUSD, the EGARCH (1, 1) was selected as the best model. Finally, VaR results are back-tested using Kupiec test. The results were accepted for the EURUSD, GBPUSD and Bitcoin at all confidence levels. As for the CNYUSD, the results were rejected at 90% and 95%confidence levels. Ripple’s results were only accepted at 90% and 99% confidence levels. Research Limitations/Implications: In this study, we only considered the EWMA, GARCH (1, 1), GARCH (p, q) and EGARCH (1, 1) models, whereby there are other models that could be used. Also, when calculating VaR, we solely examined incorporating volatility update into the historical simulation model, while disregarding other models. Furthermore, when calculating the volatility and VaR, altering the number of generated scenarios and the sample size might have led to different results. Finally, we only back-tested VaR results using the Kupiec test. Other tests might have been applied such as the independence test suggested by Christoffersen, where consecutive and frequent exceptions are taken into consideration. Practical Implications: Our results are helpful for decision makers (investors, firms, governments, etc.) willing to invest in cryptocurrencies. Bitcoin and generally cryptocurrencies cannot act as alternatives to fiat currencies at the moment. This is due to their volatile behavior significantly different from the fiat currencies behavior. Second, investors need to be prudent when considering an investment in cryptocurrencies, given their high risk and extremely volatile behavior. Finally, market participants aiming at diversifying their portfolios or seeking a risky position could consider cryptocurrencies, given their unique behavior compared to other instruments. Originality/Value: This study is original since it tackles two cryptocurrencies and three fiat currencies by comparing their volatility and VaR behavior. To our knowledge, this is the first time the GARCH (p, q) and incorporating volatility into historical simulation are used in cryptocurrencies assessment for the period March 01, 2016 through February 28, 2019.