Stochastic Calculus in Financial Modeling: A Review with Applications

Murari Ambati

No 6n9cb_v1, OSF Preprints from Center for Open Science

Abstract: 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.

Date: 2025-02-28
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Persistent link: https://EconPapers.repec.org/RePEc:osf:osfxxx:6n9cb_v1

DOI: 10.31219/osf.io/6n9cb_v1

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