An effective risk management program requires reliable risk measurement. Failure to assess inherited risks in mortgage-backed securities in the U.S. market contributed to the financial crisis of 2007–2008, which has prompted government regulators to pay greater attention to controlling risk in banks, investment funds, credit unions, and other financial institutions to prevent bankruptcy and financial crisis in the future. In order to calculate risk in a reliable manner, this thesis has focused on the statistical modeling of expected return and volatility. The primary aim of this study is to propose a framework, based on the probabilistic reduction approach, to reliably quantify market risk using statistical models and historical data. Particular emphasis is placed on the importance of the validity of the probabilistic assumptions in risk measurement by demonstrating how a statistically misspecified model will lead the evaluation of risk astray. The concept of market risk is explained by discussing the narrow definition of risk in a financial context and its evaluation and implications for financial management. After highlighting empirical evidence and discussing the limitations of the ARCH-GARCH-type volatility models using exchange rate and stock market data, we proposed Student's t Autoregressive models to estimate expected return and volatility to measure risk, using Value at Risk (VaR) and Expected Shortfall (ES). The misspecification testing analysis shows that our proposed models can adequately capture the chance regularities in exchange rates and stock indexes data and give a reliable estimation of regression and skedastic functions used in risk measurement. According to empirical findings, the COVID-19 pandemic in the first quarter of 2020 posed an enormous risk to global financial markets. The risk in financial markets returned to levels prior to the COVID-19 pandemic in 2021, after COVID-19 vaccine distribution started in developed countries. / Doctor of Philosophy / Reliable risk measurement is necessary for any effective risk management program. Hence, the primary purpose of this dissertation was to propose a framework to quantify market risk using statistical models and historical data, with a particular emphasis placed on checking the validity of probabilistic assumptions underlying models. After discussing the concept of market risk and its evaluation methods in financial management, we explored the empirical evidence in financial data and highlighted some limitations of other well-known modeling approaches. In order to ameliorate limitations, this study proposed Student's t Autoregressive models to estimate the conditional mean and the conditional variance of the financial variables and use them to measure risk via two popular methods: Value at Risk (VaR) and Expected Shortfall (ES). Further investigation shows that our proposed models can adequately model exchange rates and stock indexes data and give reliable estimations to use in risk measurement. We used our model to quantify risk in global financial markets in recent years. The results show that the COVID-19 pandemic posed an enormous risk to global financial markets in the first quarter of 2020. In 2021, the level of risk in financial markets returned to levels before the COVID-19 pandemic, after COVID-19 vaccine distribution started in developed countries.