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• Lecture #1: Introduction to Financial Derivatives


• Lecture #2: Financial Option Valuation Preliminaries


• Lecture #3: Normal and Lognormal Random Variables


• Lecture #4, 5, 6: Discrete-Time Martingales


• Lecture #7, 8: Brownian Motion as a Model of a Fair Game


• Lecture #9, 10: Riemann Integration


• Lecture #11: The Riemann Integral of Brownian Motion


• Lecture #12: Wiener Integration


• Lecture #13: Calculating Wiener Integrals


• Lecture #14: Further Properties of the Wiener Integral


• Lecture #15: Itô Integration (Part I)


• Lecture #16, 17: Itô Integration (Part II)


• Lecture #18, 19: Itô's Formula (Part I)


• Lecture #20, 21, 22: Itô's Formula (Part II)


• Lecture #23, 24, 25: Deriving the Black-Scholes Partial Differential Equation


• Lecture #26, 27: Solving the Black-Scholes Partial Differential Equation


• Lecture #28: Calculations with Itô's Formula


• Lecture #29: The Greeks


• Lecture #30: Implied Volatility


• Lecture #31, 32: The Ornstein-Uhlenbeck Process as a Model of Volatility


• Lecture #33, 34: The Characteristic Function for a Diffusion


• Lecture #35: The Characteristic Function for Heston's Model