ABSTRACT The growing importance of green energy investments necessitates understanding their dynamic behavior and market efficiency, particularly during geopolitical instability. This study examines the performance of three major green energy indices – First Trust NASDAQ Clean Edge Green Energy Index Fund, Invesco Wilder Hill Clean Energy, and S&P Global Clean Energy Index – across distinct macroeconomic periods, including the post-Paris Agreement era, COVID-19 pandemic, Russia-Ukraine conflict, and Israel-Gaza conflict. We apply two advanced stochastic modeling techniques to address the complexities of price movements in these indices: Geometric Brownian Motion and Multifractional Brownian Motion. The Hurst exponent is calculated to evaluate market memory and efficiency during these periods. Our findings demonstrate that while the Geometric Brownian Motion model effectively captures general market trends, the Multifractional Brownian Motion model reflects the nuanced volatilities and structural shifts in green energy markets, particularly during heightened geopolitical tension. The Hurst analysis identifies alternating periods of persistence and anti-persistence, highlighting varying levels of market efficiency and partially challenging the Efficient Market Hypothesis. This study’s novelty lies in applying Geometric Brownian Motion and Multifractional Brownian Motion to green energy indices, providing a comprehensive approach to analyzing their behavior under external shocks. These results contribute to the literature by offering insights into the resilience and efficiency of green energy investments, thus aiding investors and policymakers in navigating the complexities of sustainable finance during global crises.
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