RIEMANNIAN APPROACH TO MAPPING CRYPTOCURRENCY IN THE FINANCIAL MARKET

Abstract

The valuation of the cryptocurrency market surpassed three trillion dollars in 2022, underscoring the burgeoning interest in digital currencies and decentralized finance.In response, on June 7, 2022, a bipartisan initiative led to the introduction of the "Responsible Financial Innovation Act," positioning cryptocurrencies as commodities and designating the Commodity Futures Trading Commission as the primary regulatory authority for the cryptocurrency market.Intriguingly, a study by Kim et al. (2022, JABE & IJBR) utilized a non-Euclidean methodology, suggesting that cryptocurrencies, in terms of their price dynamics, resemble securities more than commodities.However, a critical assessment of Kim et al. (2022, IJBR) reveals a methodological gap: the non-Euclidean distances were employed to derive a Euclidean configuration of 28 asset classes via multi-dimensional scaling.This Euclidean structure was subsequently employed for asset class categorization using -means clustering.This approach, while acknowledging the non-Euclidean distances among the 28 asset classes, leverages a Euclidean embedding for classification.In contrast, our research employs data depth to categorize asset classes without resorting to Euclidean embedding.We compare our findings with those of Kim et al. (2022, JABE & IJBR) for a comprehensive understanding.