Author(s)

Eric M. Kimani¹, Anthony Ngunyi², Joseph K. Mungatu³

¹Department of Mathematics, Pan African University, Nairobi, Kenya.
²Department of Mathematics, Statistics and Actuarial Sciences, Dedan Kimathi University of Science and Technology, Nyeri, Kenya.
³Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya.

Cryptocurrencies are considered to be among the most disruptive innovations done in the financial sector within the last decade. It is a digital asset that is designed to serve as a medium of exchange using cryptography. Financial modeling of cryptocurrencies is needed in order to determine the presence of dependence between currencies. Copulas functions assist in modeling dependency structure by making it possible to separate marginal distributions of a given multivariate distribution. The purpose of the study was to model dependencies of cryptocurrencies using copula Garch. The study proposed the use of copula Garch model to model the dependence of cryptocurrency price data. Bivariate copula was extended to Bivariate Copula Garch in order to model prices and measure the cryptocurrency dependence. Prices of the four cryptocurrencies (Bitcoin, Binance, Litecoin and Dogecoin) were analyzed to establish whether there exists any dependency. The results showed standard Garch (1,1) under the highly flexible ARMA-GARCH model was appropriate to identify the true patterns of index returns. Fitting the copula standard Garch (1,1) model to the currencies, it was observed that the pair Litecoin and Bitcoin has the highest tail dependence among the selected cryptocurrencies, which implies that change in prices of Litecoin will influence the prices of Bitcoin and vice versa is true. Optimization of the cryptocurrencies showed that Dogecoin has the best optimization. The results of this study indicate that investing on Dogecoin significantly reduces risk irrespective of significant correlation among Litecoin, Bitcoin and Binance. Standard Garch (1,1) is the best in identifying dependence between the cryptocurrencies.

Cryptocurrency, Copula Garch, GARCH-Model, Dependence

Kimani, E. , Ngunyi, A. and Mungatu, J. (2023) Modelling Dependence of Cryptocurrencies Using Copula Garch. Journal of Mathematical Finance, 13, 321-338. doi: 10.4236/jmf.2023.133020.