Nowadays, financial derivatives play an increasingly important role in the global financial system, and options are popular structural financial derivatives, which attract much attention from academia and the industry. China Financial Futures Exchange (CFFEX) initiated the CSI 1000 index future and CSI 1000 index option in the Chinese market on July 22, 2022, which indicates a trend of acceleration in financial innovations in China’s financial market. This dissertation focuses on the volatility models in option pricing and modern numerical procedures that approximate option prices. In this dissertation, different stochastic volatility models, for example, the Black–Scholes model and the Heston stochastic volatility model, are introduced and applied to price in not only European options but also exotic options, which possess complicated payoff structures. Moreover, a comprehensive empirical analysis is conducted to demonstrate these option pricing algorithms based on the recent data of CSI 1000 index options in the Chinese market. / Business Administration/Finance