Stochastic Volatility Models and Their Applications to Financial Markets

Volatility plays an essential role in financial markets. It influences asset valuation, risk control, and investment planning. Conventional models, such as the Black-Scholes model, assume a constant volatility, but this does not hold in actual markets where volatility fluctuates over time. This paper studies stochastic volatility models, which allow volatility to change. These models can better reflect real market conditions. By reviewing the literature, this paper discusses common stochastic volatility models, including the GARCH, Heston, and SABR models. The study shows that these models have clear advantages over traditional models when pricing derivatives and managing risk. This research provides new insights into volatility modeling and points to future directions for both theory and practice. Moreover, this paper explores the limitations of stochastic volatility models, acknowledging the trade-offs between complexity and practicality. While models like GARCH and Heston are highly effective in capturing time-varying volatility and improving the accuracy of derivative pricing, they are often computationally intensive and require advanced estimation techniques.