Demand for Sustainable, Climate, Social finance has gained momentum after the COP 21 agreement and paved the way by adopting United Nations Sustainable Development Goals for the sustainable development in all dimensions of the global society. The global corporate world working onenvironmental, social, and economic aspectsof business operational practices.The UN’s sustainable stock exchange (SSE) initiative (2009)has adopted five (SDGs 5, 8, 10, 12 & 13) SDGs for global stock exchanges.The paper examines the sustainability practices and volatility nature and leverage effect of sustainability indices inIndia, Russia, and Luxembourg stock exchanges.For the analysisdata has taken from2015 to2021 and analysed by using unit root test, ARCH/GARCH family models,Johansen co-integration test.The results indicate that the sustainability indices perform well and investors can diversify their portfolios to minimizing risk through responsible investment. The study finds that the higher volatility prevalence in Luxembourg than Russia and India. The study also finds the leverage effect and indicates the negative news have more impact on volatility than the positive news.

KEYWORDS: UN SDGs, Sustainable Stock Exchanges, ARCH/GARCH, EGARCH.