Stochastic Calculus in Financial Modeling: A Review with Applications

Stochastic calculus has become an indispensable tool in quantitative finance, offering a robust framework for modeling the evolution of financial markets and derivative pricing. This paper provides an in-depth review of stochastic calculus and its applications in financial modeling, with a focus on key concepts such as stochastic differential equations (SDEs), Ito’s Lemma, and the Black-Scholes-Merton model. We explore how mathematical tools are used for price dynamics, volatility, and interest rates. Advanced models such as stochastic volatility models and jump-diffusion processes are also discussed. This paper talks into theoretical fundamentals, practical implementations, and limitations of these models in real-world financial environments.