Probability and Stochastic Calculus for Finance

Financial markets are driven by uncertainty, making probability and stochastic calculus essential tools for anyone looking to understand modern quantitative finance. This text-based course guides you through the mathematical frameworks used to model asset prices, analyze risk, and value financial derivatives. You will transition from basic probability concepts to the complex continuous-time models used by industry professionals today. By completing this course, you will develop a strong intuitive and mathematical grasp of how randomness is modeled in financial markets, enabling you to read and evaluate quantitative finance literature and models with confidence. What you'll learn: - Understand foundational probability theory, random variables, and expectation in a financial context - Master the mechanics of random walks and discrete-time binomial asset pricing models - Explore Brownian motion and its critical role in continuous-time financial modeling - Apply Ito's Lemma to derive and solve stochastic differential equations - Grasp the concepts of arbitrage, market completeness, and risk-neutral pricing - Analyze the Black-Scholes-Merton framework from a stochastic perspective This course begins with essential mathematical definitions and core probability concepts before moving systematically into stochastic processes and financial applications. Through structured written lessons and practical mathematical exercises, you will build your quantitative skills from the ground up. This course is designed for beginners to quantitative finance, including students, aspiring analysts, and professionals looking to build a rigorous mathematical foundation. Prior exposure to basic calculus is helpful, but no advanced background in finance or probability is required.