Modeling Sustainable Development of Cryptocurrencies by a Fractional Pure-Jump Process in DEA Framework

Navideh Modarresi; Moshtagh Darvishi; Shokoofeh Banihashemi

doi:10.31181/ijes1412025178

Authors

Navideh Modarresi Department of Mathematics, Faculty of Statistics, Mathematics and Computer science, Allameh Tabataba'i University, Tehran, Iran Author https://orcid.org/0000-0003-0229-2011
Moshtagh Darvishi Department of Finance and Banking, Allameh Tabataba'i University, Tehran, Iran Author
Shokoofeh Banihashemi Department of Mathematics, Faculty of Statistics, Mathematics and Computer science, Allameh Tabataba'i University, Tehran, Iran Author https://orcid.org/0000-0002-6947-0284

DOI:

https://doi.org/10.31181/ijes1412025178

Keywords:

Data envelopment analysis, Fractional normal inverse Gaussian, Relative efficiency , Sustainable portfolio , Value at risk

Abstract

Sustainable cryptocurrency modeling is vital for maximizing both economic and environmental benefits amid significant investor interest. This research develops a comprehensive methodology for cryptocurrency selection by holistically integrating financial aspects, such as returns and risk, with environmental sustainability. To quantify risk and further evaluate cryptocurrency efficiency, we employ an ARMA-GARCH model with fractional normal inverse Gaussian (FNIG) innovations to forecast Value at Risk (VaR) and expected returns. Subsequently, we apply Data Envelopment Analysis (DEA) to identify the most efficient cryptocurrencies, incorporating mining costs and the forecasted VaR as inputs—representing energy cost and risk, respectively—while using the forecasted expected returns as the output. This approach enables a direct comparison of cryptocurrencies based on these critical factors. Our findings demonstrate that accounting for the inherent stochastic behavior of cryptocurrencies leads to more accurate estimations, and the DEA highlights the essential role of energy costs in selecting efficient cryptocurrencies.

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