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In this study, we modeled the log-return of three emerging markets' stock indices, namely, Shanghai SSE, Russia MOEX, and Bombay Stock Exchange Sensex using the generalized hyperbolic family of distributions. We found the generalized hyperbolic family of distributions as the best fit for describing the probability density based on AIC and likelihood ratio test. The coherent risk measure, i.e., the expected shortfall, predicted using the best fit probability distribution, was used as a market risk quantification metric. During the COVID-19 period, the Indian stock market showed maximum market risk, followed by the Russian. The Chinese market showed the least market risk. Our experiment demonstrated a significant (p = 0.000) difference in the three markets concerning the coherent risk at different probability levels from 0.001 to 0.05 in the COVID-19 period using the Jonckheere-Terpstra test. The coherent market risk increased substantially in the Indian and Russian markets during the COVID-19 pandemic compared to the pre-COVID-19 period. However, in the Chinese market, we found that the coherent risk decreased during the COVID-19 period compared to the pre-COVID-19 period. We carried out the empirical study using the adjusted daily closing values of SSE, MOEX, and Sensex from July 2018 to July 2021 and dividing the data sets into pre-COVID-19 and COVID-19 periods based on the first emergence of the COVID-19 case.